KILLED proof of input_6H7Cbmgixr.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 13 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 7 ms] (16) CpxRNTS (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 200 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 70 ms] (24) CpxRNTS (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 255 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 57 ms] (30) CpxRNTS (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 183 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 86 ms] (36) CpxRNTS (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 180 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 5 ms] (42) CpxRNTS (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 23.8 s] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 7636 ms] (48) CpxRNTS (49) CompletionProof [UPPER BOUND(ID), 0 ms] (50) CpxTypedWeightedCompleteTrs (51) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (52) CpxRNTS (53) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (54) CdtProblem (55) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (56) CdtProblem (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 11 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1 ms] (70) CdtProblem (71) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 84 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms] (90) CdtProblem (91) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 3 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms] (96) CdtProblem (97) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6 ms] (102) CdtProblem (103) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 386 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 338 ms] (110) CdtProblem (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms] (124) CdtProblem (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms] (144) CdtProblem (145) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem (179) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (184) CdtProblem (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (186) CdtProblem (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms] (188) CdtProblem (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (190) CdtProblem (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms] (192) CdtProblem (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (194) CdtProblem (195) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (196) CdtProblem (197) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (200) CdtProblem (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (202) CdtProblem (203) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (204) CdtProblem (205) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (206) CdtProblem (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (208) CdtProblem (209) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 3 ms] (210) CdtProblem (211) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 28 ms] (212) CdtProblem (213) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (214) CdtProblem (215) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms] (216) CdtProblem (217) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (218) CdtProblem (219) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (220) CdtProblem (221) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (222) CdtProblem (223) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (224) CdtProblem (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (226) CdtProblem (227) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (228) CdtProblem (229) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (230) CdtProblem (231) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (232) CdtProblem (233) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (234) CdtProblem (235) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (236) CdtProblem (237) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms] (238) CdtProblem (239) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 14 ms] (240) CdtProblem (241) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (242) CdtProblem (243) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (244) CdtProblem (245) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (246) CdtProblem (247) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (248) CdtProblem (249) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (250) CdtProblem (251) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1 ms] (252) CdtProblem (253) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (254) CdtProblem (255) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (256) CdtProblem (257) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (258) CdtProblem (259) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 16 ms] (260) CdtProblem (261) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (262) CdtProblem (263) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (264) CdtProblem (265) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (266) CdtProblem (267) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (268) CdtProblem (269) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (270) CdtProblem (271) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (272) CdtProblem (273) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (274) CdtProblem (275) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (276) CdtProblem (277) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (278) CdtProblem (279) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (280) CdtProblem ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(x)))) -> check(s(x)) half(0) -> 0 half(s(0)) -> 0 half(s(s(x))) -> s(half(x)) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) times(x, y) -> timesIter(x, y, 0) timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y)) p(s(x)) -> x p(0) -> 0 if(zero, x, y, z, u) -> z if(odd, x, y, z, u) -> timesIter(p(x), y, u) if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z)))) 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: check(0') -> zero check(s(0')) -> odd check(s(s(0'))) -> even check(s(s(s(x)))) -> check(s(x)) half(0') -> 0' half(s(0')) -> 0' half(s(s(x))) -> s(half(x)) plus(0', y) -> y plus(s(x), y) -> s(plus(x, y)) times(x, y) -> timesIter(x, y, 0') timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y)) p(s(x)) -> x p(0') -> 0' if(zero, x, y, z, u) -> z if(odd, x, y, z, u) -> timesIter(p(x), y, u) if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z)))) 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: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(x)))) -> check(s(x)) half(0) -> 0 half(s(0)) -> 0 half(s(s(x))) -> s(half(x)) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) times(x, y) -> timesIter(x, y, 0) timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y)) p(s(x)) -> x p(0) -> 0 if(zero, x, y, z, u) -> z if(odd, x, y, z, u) -> timesIter(p(x), y, u) if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z)))) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: check(0) -> zero [1] check(s(0)) -> odd [1] check(s(s(0))) -> even [1] check(s(s(s(x)))) -> check(s(x)) [1] half(0) -> 0 [1] half(s(0)) -> 0 [1] half(s(s(x))) -> s(half(x)) [1] plus(0, y) -> y [1] plus(s(x), y) -> s(plus(x, y)) [1] times(x, y) -> timesIter(x, y, 0) [1] timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y)) [1] p(s(x)) -> x [1] p(0) -> 0 [1] if(zero, x, y, z, u) -> z [1] if(odd, x, y, z, u) -> timesIter(p(x), y, u) [1] if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z)))) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: check(0) -> zero [1] check(s(0)) -> odd [1] check(s(s(0))) -> even [1] check(s(s(s(x)))) -> check(s(x)) [1] half(0) -> 0 [1] half(s(0)) -> 0 [1] half(s(s(x))) -> s(half(x)) [1] plus(0, y) -> y [1] plus(s(x), y) -> s(plus(x, y)) [1] times(x, y) -> timesIter(x, y, 0) [1] timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y)) [1] p(s(x)) -> x [1] p(0) -> 0 [1] if(zero, x, y, z, u) -> z [1] if(odd, x, y, z, u) -> timesIter(p(x), y, u) [1] if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z)))) [1] The TRS has the following type information: check :: 0:s -> zero:odd:even 0 :: 0:s zero :: zero:odd:even s :: 0:s -> 0:s odd :: zero:odd:even even :: zero:odd:even half :: 0:s -> 0:s plus :: 0:s -> 0:s -> 0:s times :: 0:s -> 0:s -> 0:s timesIter :: 0:s -> 0:s -> 0:s -> 0:s if :: zero:odd:even -> 0:s -> 0:s -> 0:s -> 0:s -> 0:s p :: 0:s -> 0:s Rewrite Strategy: INNERMOST ---------------------------------------- (9) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: times_2 (c) The following functions are completely defined: check_1 plus_2 timesIter_3 half_1 p_1 if_5 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: check(0) -> zero [1] check(s(0)) -> odd [1] check(s(s(0))) -> even [1] check(s(s(s(x)))) -> check(s(x)) [1] half(0) -> 0 [1] half(s(0)) -> 0 [1] half(s(s(x))) -> s(half(x)) [1] plus(0, y) -> y [1] plus(s(x), y) -> s(plus(x, y)) [1] times(x, y) -> timesIter(x, y, 0) [1] timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y)) [1] p(s(x)) -> x [1] p(0) -> 0 [1] if(zero, x, y, z, u) -> z [1] if(odd, x, y, z, u) -> timesIter(p(x), y, u) [1] if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z)))) [1] The TRS has the following type information: check :: 0:s -> zero:odd:even 0 :: 0:s zero :: zero:odd:even s :: 0:s -> 0:s odd :: zero:odd:even even :: zero:odd:even half :: 0:s -> 0:s plus :: 0:s -> 0:s -> 0:s times :: 0:s -> 0:s -> 0:s timesIter :: 0:s -> 0:s -> 0:s -> 0:s if :: zero:odd:even -> 0:s -> 0:s -> 0:s -> 0:s -> 0:s p :: 0:s -> 0:s Rewrite Strategy: INNERMOST ---------------------------------------- (11) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (12) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: check(0) -> zero [1] check(s(0)) -> odd [1] check(s(s(0))) -> even [1] check(s(s(s(x)))) -> check(s(x)) [1] half(0) -> 0 [1] half(s(0)) -> 0 [1] half(s(s(x))) -> s(half(x)) [1] plus(0, y) -> y [1] plus(s(x), y) -> s(plus(x, y)) [1] times(x, y) -> timesIter(x, y, 0) [1] timesIter(0, y, 0) -> if(zero, 0, y, 0, y) [3] timesIter(0, y, s(x'')) -> if(zero, 0, y, s(x''), s(plus(x'', y))) [3] timesIter(s(0), y, 0) -> if(odd, s(0), y, 0, y) [3] timesIter(s(0), y, s(x1)) -> if(odd, s(0), y, s(x1), s(plus(x1, y))) [3] timesIter(s(s(0)), y, 0) -> if(even, s(s(0)), y, 0, y) [3] timesIter(s(s(0)), y, s(x2)) -> if(even, s(s(0)), y, s(x2), s(plus(x2, y))) [3] timesIter(s(s(s(x'))), y, 0) -> if(check(s(x')), s(s(s(x'))), y, 0, y) [3] timesIter(s(s(s(x'))), y, s(x3)) -> if(check(s(x')), s(s(s(x'))), y, s(x3), s(plus(x3, y))) [3] p(s(x)) -> x [1] p(0) -> 0 [1] if(zero, x, y, z, u) -> z [1] if(odd, s(x4), y, z, u) -> timesIter(x4, y, u) [2] if(odd, 0, y, z, u) -> timesIter(0, y, u) [2] if(even, 0, y, 0, u) -> plus(timesIter(0, y, 0), timesIter(0, y, 0)) [5] if(even, 0, y, s(0), u) -> plus(timesIter(0, y, 0), timesIter(0, y, s(half(0)))) [5] if(even, 0, y, s(s(x6)), u) -> plus(timesIter(0, y, s(half(x6))), timesIter(0, y, s(half(s(x6))))) [5] if(even, s(0), y, 0, u) -> plus(timesIter(0, y, 0), timesIter(0, y, 0)) [5] if(even, s(0), y, s(0), u) -> plus(timesIter(0, y, 0), timesIter(0, y, s(half(0)))) [5] if(even, s(0), y, s(s(x7)), u) -> plus(timesIter(0, y, s(half(x7))), timesIter(0, y, s(half(s(x7))))) [5] if(even, s(s(x5)), y, 0, u) -> plus(timesIter(s(half(x5)), y, 0), timesIter(s(half(x5)), y, 0)) [5] if(even, s(s(x5)), y, s(0), u) -> plus(timesIter(s(half(x5)), y, 0), timesIter(s(half(x5)), y, s(half(0)))) [5] if(even, s(s(x5)), y, s(s(x8)), u) -> plus(timesIter(s(half(x5)), y, s(half(x8))), timesIter(s(half(x5)), y, s(half(s(x8))))) [5] The TRS has the following type information: check :: 0:s -> zero:odd:even 0 :: 0:s zero :: zero:odd:even s :: 0:s -> 0:s odd :: zero:odd:even even :: zero:odd:even half :: 0:s -> 0:s plus :: 0:s -> 0:s -> 0:s times :: 0:s -> 0:s -> 0:s timesIter :: 0:s -> 0:s -> 0:s -> 0:s if :: zero:odd:even -> 0:s -> 0:s -> 0:s -> 0:s -> 0:s p :: 0:s -> 0:s Rewrite Strategy: INNERMOST ---------------------------------------- (13) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 zero => 2 odd => 1 even => 0 ---------------------------------------- (14) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 }-> check(1 + x) :|: x >= 0, z' = 1 + (1 + (1 + x)) check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 }-> 1 + half(x) :|: x >= 0, z' = 1 + (1 + x) if(z', z'', z1, z2, z3) -{ 1 }-> z :|: z1 = y, z >= 0, z' = 2, z2 = z, x >= 0, y >= 0, z'' = x, z3 = u, u >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(x4, y, u) :|: z1 = y, x4 >= 0, z >= 0, z'' = 1 + x4, z2 = z, y >= 0, z' = 1, z3 = u, u >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, y, u) :|: z'' = 0, z1 = y, z >= 0, z2 = z, y >= 0, z' = 1, z3 = u, u >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, y, 0), timesIter(0, y, 0)) :|: z'' = 0, z1 = y, z2 = 0, y >= 0, z3 = u, z' = 0, u >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, y, 0), timesIter(0, y, 0)) :|: z1 = y, z2 = 0, y >= 0, z'' = 1 + 0, z3 = u, z' = 0, u >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, y, 0), timesIter(0, y, 1 + half(0))) :|: z'' = 0, z1 = y, z2 = 1 + 0, y >= 0, z3 = u, z' = 0, u >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, y, 0), timesIter(0, y, 1 + half(0))) :|: z1 = y, z2 = 1 + 0, y >= 0, z'' = 1 + 0, z3 = u, z' = 0, u >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, y, 1 + half(x6)), timesIter(0, y, 1 + half(1 + x6))) :|: z'' = 0, z1 = y, y >= 0, x6 >= 0, z2 = 1 + (1 + x6), z3 = u, z' = 0, u >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, y, 1 + half(x7)), timesIter(0, y, 1 + half(1 + x7))) :|: z1 = y, x7 >= 0, y >= 0, z'' = 1 + 0, z3 = u, z' = 0, z2 = 1 + (1 + x7), u >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(x5), y, 0), timesIter(1 + half(x5), y, 0)) :|: z1 = y, x5 >= 0, z2 = 0, y >= 0, z'' = 1 + (1 + x5), z3 = u, z' = 0, u >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(x5), y, 0), timesIter(1 + half(x5), y, 1 + half(0))) :|: z1 = y, z2 = 1 + 0, x5 >= 0, y >= 0, z'' = 1 + (1 + x5), z3 = u, z' = 0, u >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(x5), y, 1 + half(x8)), timesIter(1 + half(x5), y, 1 + half(1 + x8))) :|: z1 = y, x5 >= 0, x8 >= 0, y >= 0, z2 = 1 + (1 + x8), z'' = 1 + (1 + x5), z3 = u, z' = 0, u >= 0 p(z') -{ 1 }-> x :|: z' = 1 + x, x >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 plus(z', z'') -{ 1 }-> y :|: z'' = y, y >= 0, z' = 0 plus(z', z'') -{ 1 }-> 1 + plus(x, y) :|: z' = 1 + x, z'' = y, x >= 0, y >= 0 times(z', z'') -{ 1 }-> timesIter(x, y, 0) :|: z' = x, z'' = y, x >= 0, y >= 0 timesIter(z', z'', z1) -{ 3 }-> if(check(1 + x'), 1 + (1 + (1 + x')), y, 0, y) :|: z' = 1 + (1 + (1 + x')), z1 = 0, z'' = y, x' >= 0, y >= 0 timesIter(z', z'', z1) -{ 3 }-> if(check(1 + x'), 1 + (1 + (1 + x')), y, 1 + x3, 1 + plus(x3, y)) :|: z' = 1 + (1 + (1 + x')), z'' = y, x' >= 0, y >= 0, z1 = 1 + x3, x3 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, y, 0, y) :|: z1 = 0, z'' = y, y >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, y, 1 + x'', 1 + plus(x'', y)) :|: z1 = 1 + x'', z'' = y, y >= 0, x'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, y, 0, y) :|: z1 = 0, z'' = y, y >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, y, 1 + x1, 1 + plus(x1, y)) :|: x1 >= 0, z'' = y, y >= 0, z' = 1 + 0, z1 = 1 + x1 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), y, 0, y) :|: z1 = 0, z' = 1 + (1 + 0), z'' = y, y >= 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), y, 1 + x2, 1 + plus(x2, y)) :|: z' = 1 + (1 + 0), z'' = y, y >= 0, x2 >= 0, z1 = 1 + x2 ---------------------------------------- (15) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (16) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 }-> check(1 + (z' - 3)) :|: z' - 3 >= 0 check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 }-> 1 + half(z' - 2) :|: z' - 2 >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 0)) :|: z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 1 + half(0))) :|: z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 1 + half(z2 - 2)), timesIter(1 + half(z'' - 2), z1, 1 + half(1 + (z2 - 2)))) :|: z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0 plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0 plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0 times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: z1 = 0, z' - 3 >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0 ---------------------------------------- (17) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID)) Found the following analysis order by SCC decomposition: { check } { half } { plus } { p } { timesIter, if } { times } ---------------------------------------- (18) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 }-> check(1 + (z' - 3)) :|: z' - 3 >= 0 check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 }-> 1 + half(z' - 2) :|: z' - 2 >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 0)) :|: z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 1 + half(0))) :|: z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 1 + half(z2 - 2)), timesIter(1 + half(z'' - 2), z1, 1 + half(1 + (z2 - 2)))) :|: z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0 plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0 plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0 times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: z1 = 0, z' - 3 >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0 Function symbols to be analyzed: {check}, {half}, {plus}, {p}, {timesIter,if}, {times} ---------------------------------------- (19) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (20) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 }-> check(1 + (z' - 3)) :|: z' - 3 >= 0 check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 }-> 1 + half(z' - 2) :|: z' - 2 >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 0)) :|: z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 1 + half(0))) :|: z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 1 + half(z2 - 2)), timesIter(1 + half(z'' - 2), z1, 1 + half(1 + (z2 - 2)))) :|: z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0 plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0 plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0 times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: z1 = 0, z' - 3 >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0 Function symbols to be analyzed: {check}, {half}, {plus}, {p}, {timesIter,if}, {times} ---------------------------------------- (21) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: check after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 2 ---------------------------------------- (22) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 }-> check(1 + (z' - 3)) :|: z' - 3 >= 0 check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 }-> 1 + half(z' - 2) :|: z' - 2 >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 0)) :|: z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 1 + half(0))) :|: z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 1 + half(z2 - 2)), timesIter(1 + half(z'' - 2), z1, 1 + half(1 + (z2 - 2)))) :|: z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0 plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0 plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0 times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: z1 = 0, z' - 3 >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0 Function symbols to be analyzed: {check}, {half}, {plus}, {p}, {timesIter,if}, {times} Previous analysis results are: check: runtime: ?, size: O(1) [2] ---------------------------------------- (23) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: check after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 2 + z' ---------------------------------------- (24) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 }-> check(1 + (z' - 3)) :|: z' - 3 >= 0 check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 }-> 1 + half(z' - 2) :|: z' - 2 >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 0)) :|: z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 1 + half(0))) :|: z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 1 + half(z2 - 2)), timesIter(1 + half(z'' - 2), z1, 1 + half(1 + (z2 - 2)))) :|: z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0 plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0 plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0 times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: z1 = 0, z' - 3 >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0 Function symbols to be analyzed: {half}, {plus}, {p}, {timesIter,if}, {times} Previous analysis results are: check: runtime: O(n^1) [2 + z'], size: O(1) [2] ---------------------------------------- (25) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0 check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 }-> 1 + half(z' - 2) :|: z' - 2 >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 0)) :|: z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 1 + half(0))) :|: z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 1 + half(z2 - 2)), timesIter(1 + half(z'' - 2), z1, 1 + half(1 + (z2 - 2)))) :|: z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0 plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0 plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0 times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0 Function symbols to be analyzed: {half}, {plus}, {p}, {timesIter,if}, {times} Previous analysis results are: check: runtime: O(n^1) [2 + z'], size: O(1) [2] ---------------------------------------- (27) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using KoAT for: half after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z' ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0 check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 }-> 1 + half(z' - 2) :|: z' - 2 >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 0)) :|: z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 1 + half(0))) :|: z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 1 + half(z2 - 2)), timesIter(1 + half(z'' - 2), z1, 1 + half(1 + (z2 - 2)))) :|: z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0 plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0 plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0 times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0 Function symbols to be analyzed: {half}, {plus}, {p}, {timesIter,if}, {times} Previous analysis results are: check: runtime: O(n^1) [2 + z'], size: O(1) [2] half: runtime: ?, size: O(n^1) [z'] ---------------------------------------- (29) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: half after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 2 + z' ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0 check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 }-> 1 + half(z' - 2) :|: z' - 2 >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 0)) :|: z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 1 + half(0))) :|: z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 1 + half(z2 - 2)), timesIter(1 + half(z'' - 2), z1, 1 + half(1 + (z2 - 2)))) :|: z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0 plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0 plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0 times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0 Function symbols to be analyzed: {plus}, {p}, {timesIter,if}, {times} Previous analysis results are: check: runtime: O(n^1) [2 + z'], size: O(1) [2] half: runtime: O(n^1) [2 + z'], size: O(n^1) [z'] ---------------------------------------- (31) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0 check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0 plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0 plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0 times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0 Function symbols to be analyzed: {plus}, {p}, {timesIter,if}, {times} Previous analysis results are: check: runtime: O(n^1) [2 + z'], size: O(1) [2] half: runtime: O(n^1) [2 + z'], size: O(n^1) [z'] ---------------------------------------- (33) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: plus after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z' + z'' ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0 check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0 plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0 plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0 times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0 Function symbols to be analyzed: {plus}, {p}, {timesIter,if}, {times} Previous analysis results are: check: runtime: O(n^1) [2 + z'], size: O(1) [2] half: runtime: O(n^1) [2 + z'], size: O(n^1) [z'] plus: runtime: ?, size: O(n^1) [z' + z''] ---------------------------------------- (35) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: plus after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 1 + z' ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0 check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0 plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0 plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0 times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0 Function symbols to be analyzed: {p}, {timesIter,if}, {times} Previous analysis results are: check: runtime: O(n^1) [2 + z'], size: O(1) [2] half: runtime: O(n^1) [2 + z'], size: O(n^1) [z'] plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z' + z''] ---------------------------------------- (37) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (38) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0 check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0 plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0 plus(z', z'') -{ 1 + z' }-> 1 + s17 :|: s17 >= 0, s17 <= z' - 1 + z'', z' - 1 >= 0, z'' >= 0 times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' + z1 }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + s21) :|: s21 >= 0, s21 <= z1 - 1 + z'', s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + s18) :|: s18 >= 0, s18 <= z1 - 1 + z'', z'' >= 0, z1 - 1 >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + s19) :|: s19 >= 0, s19 <= z1 - 1 + z'', z1 - 1 >= 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + s20) :|: s20 >= 0, s20 <= z1 - 1 + z'', z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0 Function symbols to be analyzed: {p}, {timesIter,if}, {times} Previous analysis results are: check: runtime: O(n^1) [2 + z'], size: O(1) [2] half: runtime: O(n^1) [2 + z'], size: O(n^1) [z'] plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z' + z''] ---------------------------------------- (39) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using KoAT for: p after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z' ---------------------------------------- (40) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0 check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0 plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0 plus(z', z'') -{ 1 + z' }-> 1 + s17 :|: s17 >= 0, s17 <= z' - 1 + z'', z' - 1 >= 0, z'' >= 0 times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' + z1 }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + s21) :|: s21 >= 0, s21 <= z1 - 1 + z'', s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + s18) :|: s18 >= 0, s18 <= z1 - 1 + z'', z'' >= 0, z1 - 1 >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + s19) :|: s19 >= 0, s19 <= z1 - 1 + z'', z1 - 1 >= 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + s20) :|: s20 >= 0, s20 <= z1 - 1 + z'', z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0 Function symbols to be analyzed: {p}, {timesIter,if}, {times} Previous analysis results are: check: runtime: O(n^1) [2 + z'], size: O(1) [2] half: runtime: O(n^1) [2 + z'], size: O(n^1) [z'] plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z' + z''] p: runtime: ?, size: O(n^1) [z'] ---------------------------------------- (41) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: p after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (42) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0 check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0 plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0 plus(z', z'') -{ 1 + z' }-> 1 + s17 :|: s17 >= 0, s17 <= z' - 1 + z'', z' - 1 >= 0, z'' >= 0 times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' + z1 }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + s21) :|: s21 >= 0, s21 <= z1 - 1 + z'', s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + s18) :|: s18 >= 0, s18 <= z1 - 1 + z'', z'' >= 0, z1 - 1 >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + s19) :|: s19 >= 0, s19 <= z1 - 1 + z'', z1 - 1 >= 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + s20) :|: s20 >= 0, s20 <= z1 - 1 + z'', z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0 Function symbols to be analyzed: {timesIter,if}, {times} Previous analysis results are: check: runtime: O(n^1) [2 + z'], size: O(1) [2] half: runtime: O(n^1) [2 + z'], size: O(n^1) [z'] plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z' + z''] p: runtime: O(1) [1], size: O(n^1) [z'] ---------------------------------------- (43) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (44) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0 check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0 plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0 plus(z', z'') -{ 1 + z' }-> 1 + s17 :|: s17 >= 0, s17 <= z' - 1 + z'', z' - 1 >= 0, z'' >= 0 times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' + z1 }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + s21) :|: s21 >= 0, s21 <= z1 - 1 + z'', s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + s18) :|: s18 >= 0, s18 <= z1 - 1 + z'', z'' >= 0, z1 - 1 >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + s19) :|: s19 >= 0, s19 <= z1 - 1 + z'', z1 - 1 >= 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + s20) :|: s20 >= 0, s20 <= z1 - 1 + z'', z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0 Function symbols to be analyzed: {timesIter,if}, {times} Previous analysis results are: check: runtime: O(n^1) [2 + z'], size: O(1) [2] half: runtime: O(n^1) [2 + z'], size: O(n^1) [z'] plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z' + z''] p: runtime: O(1) [1], size: O(n^1) [z'] ---------------------------------------- (45) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using KoAT for: timesIter after applying outer abstraction to obtain an ITS, resulting in: EXP with polynomial bound: ? Computed SIZE bound using CoFloCo for: if after applying outer abstraction to obtain an ITS, resulting in: INF with polynomial bound: ? ---------------------------------------- (46) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0 check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0 plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0 plus(z', z'') -{ 1 + z' }-> 1 + s17 :|: s17 >= 0, s17 <= z' - 1 + z'', z' - 1 >= 0, z'' >= 0 times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' + z1 }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + s21) :|: s21 >= 0, s21 <= z1 - 1 + z'', s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + s18) :|: s18 >= 0, s18 <= z1 - 1 + z'', z'' >= 0, z1 - 1 >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + s19) :|: s19 >= 0, s19 <= z1 - 1 + z'', z1 - 1 >= 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + s20) :|: s20 >= 0, s20 <= z1 - 1 + z'', z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0 Function symbols to be analyzed: {timesIter,if}, {times} Previous analysis results are: check: runtime: O(n^1) [2 + z'], size: O(1) [2] half: runtime: O(n^1) [2 + z'], size: O(n^1) [z'] plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z' + z''] p: runtime: O(1) [1], size: O(n^1) [z'] timesIter: runtime: ?, size: EXP if: runtime: ?, size: INF ---------------------------------------- (47) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: timesIter after applying outer abstraction to obtain an ITS, resulting in: INF with polynomial bound: ? ---------------------------------------- (48) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0 check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0 if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0 plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0 plus(z', z'') -{ 1 + z' }-> 1 + s17 :|: s17 >= 0, s17 <= z' - 1 + z'', z' - 1 >= 0, z'' >= 0 times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0 timesIter(z', z'', z1) -{ 3 + z' + z1 }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + s21) :|: s21 >= 0, s21 <= z1 - 1 + z'', s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0 timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + s18) :|: s18 >= 0, s18 <= z1 - 1 + z'', z'' >= 0, z1 - 1 >= 0, z' = 0 timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + s19) :|: s19 >= 0, s19 <= z1 - 1 + z'', z1 - 1 >= 0, z'' >= 0, z' = 1 + 0 timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0 timesIter(z', z'', z1) -{ 3 + z1 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + s20) :|: s20 >= 0, s20 <= z1 - 1 + z'', z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0 Function symbols to be analyzed: {timesIter,if}, {times} Previous analysis results are: check: runtime: O(n^1) [2 + z'], size: O(1) [2] half: runtime: O(n^1) [2 + z'], size: O(n^1) [z'] plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z' + z''] p: runtime: O(1) [1], size: O(n^1) [z'] timesIter: runtime: INF, size: EXP if: runtime: ?, size: INF ---------------------------------------- (49) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: none And the following fresh constants: none ---------------------------------------- (50) 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: check(0) -> zero [1] check(s(0)) -> odd [1] check(s(s(0))) -> even [1] check(s(s(s(x)))) -> check(s(x)) [1] half(0) -> 0 [1] half(s(0)) -> 0 [1] half(s(s(x))) -> s(half(x)) [1] plus(0, y) -> y [1] plus(s(x), y) -> s(plus(x, y)) [1] times(x, y) -> timesIter(x, y, 0) [1] timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y)) [1] p(s(x)) -> x [1] p(0) -> 0 [1] if(zero, x, y, z, u) -> z [1] if(odd, x, y, z, u) -> timesIter(p(x), y, u) [1] if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z)))) [1] The TRS has the following type information: check :: 0:s -> zero:odd:even 0 :: 0:s zero :: zero:odd:even s :: 0:s -> 0:s odd :: zero:odd:even even :: zero:odd:even half :: 0:s -> 0:s plus :: 0:s -> 0:s -> 0:s times :: 0:s -> 0:s -> 0:s timesIter :: 0:s -> 0:s -> 0:s -> 0:s if :: zero:odd:even -> 0:s -> 0:s -> 0:s -> 0:s -> 0:s p :: 0:s -> 0:s Rewrite Strategy: INNERMOST ---------------------------------------- (51) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 zero => 2 odd => 1 even => 0 ---------------------------------------- (52) Obligation: Complexity RNTS consisting of the following rules: check(z') -{ 1 }-> check(1 + x) :|: x >= 0, z' = 1 + (1 + (1 + x)) check(z') -{ 1 }-> 2 :|: z' = 0 check(z') -{ 1 }-> 1 :|: z' = 1 + 0 check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0) half(z') -{ 1 }-> 0 :|: z' = 0 half(z') -{ 1 }-> 0 :|: z' = 1 + 0 half(z') -{ 1 }-> 1 + half(x) :|: x >= 0, z' = 1 + (1 + x) if(z', z'', z1, z2, z3) -{ 1 }-> z :|: z1 = y, z >= 0, z' = 2, z2 = z, x >= 0, y >= 0, z'' = x, z3 = u, u >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> timesIter(p(x), y, u) :|: z1 = y, z >= 0, z2 = z, x >= 0, y >= 0, z'' = x, z' = 1, z3 = u, u >= 0 if(z', z'', z1, z2, z3) -{ 1 }-> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(1 + z))) :|: z1 = y, z >= 0, z2 = z, x >= 0, y >= 0, z'' = x, z3 = u, z' = 0, u >= 0 p(z') -{ 1 }-> x :|: z' = 1 + x, x >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 plus(z', z'') -{ 1 }-> y :|: z'' = y, y >= 0, z' = 0 plus(z', z'') -{ 1 }-> 1 + plus(x, y) :|: z' = 1 + x, z'' = y, x >= 0, y >= 0 times(z', z'') -{ 1 }-> timesIter(x, y, 0) :|: z' = x, z'' = y, x >= 0, y >= 0 timesIter(z', z'', z1) -{ 1 }-> if(check(x), x, y, z, plus(z, y)) :|: z1 = z, z >= 0, z' = x, z'' = y, x >= 0, y >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (53) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) times(z0, z1) -> timesIter(z0, z1, 0) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) p(s(z0)) -> z0 p(0) -> 0 if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) Tuples: CHECK(0) -> c CHECK(s(0)) -> c1 CHECK(s(s(0))) -> c2 CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(0) -> c4 HALF(s(0)) -> c5 HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(0, z0) -> c7 PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) TIMES(z0, z1) -> c9(TIMESITER(z0, z1, 0)) TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0)) TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) P(s(z0)) -> c12 P(0) -> c13 IF(zero, z0, z1, z2, z3) -> c14 IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3), P(z0)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) S tuples: CHECK(0) -> c CHECK(s(0)) -> c1 CHECK(s(s(0))) -> c2 CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(0) -> c4 HALF(s(0)) -> c5 HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(0, z0) -> c7 PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) TIMES(z0, z1) -> c9(TIMESITER(z0, z1, 0)) TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0)) TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) P(s(z0)) -> c12 P(0) -> c13 IF(zero, z0, z1, z2, z3) -> c14 IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3), P(z0)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) K tuples:none Defined Rule Symbols: check_1, half_1, plus_2, times_2, timesIter_3, p_1, if_5 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, TIMES_2, TIMESITER_3, P_1, IF_5 Compound Symbols: c, c1, c2, c3_1, c4, c5, c6_1, c7, c8_1, c9_1, c10_2, c11_2, c12, c13, c14, c15_2, c16_3, c17_3, c18_3, c19_3 ---------------------------------------- (55) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: TIMES(z0, z1) -> c9(TIMESITER(z0, z1, 0)) Removed 9 trailing nodes: P(s(z0)) -> c12 PLUS(0, z0) -> c7 CHECK(s(s(0))) -> c2 CHECK(s(0)) -> c1 IF(zero, z0, z1, z2, z3) -> c14 CHECK(0) -> c HALF(0) -> c4 P(0) -> c13 HALF(s(0)) -> c5 ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) times(z0, z1) -> timesIter(z0, z1, 0) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) p(s(z0)) -> z0 p(0) -> 0 if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0)) TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3), P(z0)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0)) TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3), P(z0)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) K tuples:none Defined Rule Symbols: check_1, half_1, plus_2, times_2, timesIter_3, p_1, if_5 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, TIMESITER_3, IF_5 Compound Symbols: c3_1, c6_1, c8_1, c10_2, c11_2, c15_2, c16_3, c17_3, c18_3, c19_3 ---------------------------------------- (57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) times(z0, z1) -> timesIter(z0, z1, 0) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) p(s(z0)) -> z0 p(0) -> 0 if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0)) TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0)) TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) K tuples:none Defined Rule Symbols: check_1, half_1, plus_2, times_2, timesIter_3, p_1, if_5 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, TIMESITER_3, IF_5 Compound Symbols: c3_1, c6_1, c8_1, c10_2, c11_2, c16_3, c17_3, c18_3, c19_3, c15_1 ---------------------------------------- (59) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: times(z0, z1) -> timesIter(z0, z1, 0) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0)) TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0)) TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) K tuples:none Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, TIMESITER_3, IF_5 Compound Symbols: c3_1, c6_1, c8_1, c10_2, c11_2, c16_3, c17_3, c18_3, c19_3, c15_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0)) by TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(0, x1, x2) -> c10(IF(zero, 0, x1, x2, plus(x2, x1)), CHECK(0)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)), CHECK(s(0))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)), CHECK(s(s(0)))) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(0, x1, x2) -> c10(IF(zero, 0, x1, x2, plus(x2, x1)), CHECK(0)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)), CHECK(s(0))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)), CHECK(s(s(0)))) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(0, x1, x2) -> c10(IF(zero, 0, x1, x2, plus(x2, x1)), CHECK(0)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)), CHECK(s(0))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)), CHECK(s(s(0)))) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) K tuples:none Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, TIMESITER_3, IF_5 Compound Symbols: c3_1, c6_1, c8_1, c11_2, c16_3, c17_3, c18_3, c19_3, c15_1, c10_2 ---------------------------------------- (63) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: TIMESITER(0, x1, x2) -> c10(IF(zero, 0, x1, x2, plus(x2, x1)), CHECK(0)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)), CHECK(s(0))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)), CHECK(s(s(0)))) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)), CHECK(s(0))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)), CHECK(s(s(0)))) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) K tuples:none Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, TIMESITER_3, IF_5 Compound Symbols: c3_1, c6_1, c8_1, c11_2, c16_3, c17_3, c18_3, c19_3, c15_1, c10_2 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) K tuples:none Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, TIMESITER_3, IF_5 Compound Symbols: c3_1, c6_1, c8_1, c11_2, c16_3, c17_3, c18_3, c19_3, c15_1, c10_2, c10_1 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) by TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0), PLUS(0, z0)) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(0, x1, x2) -> c11(IF(zero, 0, x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0), PLUS(0, z0)) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(0, x1, x2) -> c11(IF(zero, 0, x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0), PLUS(0, z0)) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(0, x1, x2) -> c11(IF(zero, 0, x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) K tuples:none Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c16_3, c17_3, c18_3, c19_3, c15_1, c10_2, c10_1, c11_2 ---------------------------------------- (69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) K tuples:none Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c16_3, c17_3, c18_3, c19_3, c15_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (71) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) We considered the (Usable) Rules: half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) half(0) -> 0 p(0) -> 0 p(s(z0)) -> z0 And the Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = [1] POL(CHECK(x_1)) = 0 POL(HALF(x_1)) = 0 POL(IF(x_1, x_2, x_3, x_4, x_5)) = x_2 + x_3 POL(PLUS(x_1, x_2)) = 0 POL(TIMESITER(x_1, x_2, x_3)) = x_1 + x_2 POL(c10(x_1)) = x_1 POL(c10(x_1, x_2)) = x_1 + x_2 POL(c11(x_1)) = x_1 POL(c11(x_1, x_2)) = x_1 + x_2 POL(c15(x_1)) = x_1 POL(c16(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(c17(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(c18(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(c19(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(c3(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(check(x_1)) = [1] POL(even) = [1] POL(half(x_1)) = x_1 POL(if(x_1, x_2, x_3, x_4, x_5)) = [1] + x_1 + x_2 + x_3 + x_4 + x_5 POL(odd) = [1] POL(p(x_1)) = x_1 POL(plus(x_1, x_2)) = [1] POL(s(x_1)) = x_1 POL(timesIter(x_1, x_2, x_3)) = [1] + x_2 POL(zero) = [1] ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c16_3, c17_3, c18_3, c19_3, c15_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) by IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c17_3, c18_3, c19_3, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c17_3, c18_3, c19_3, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) by IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c18_3, c19_3, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c18_3, c19_3, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) by IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c19_3, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c19_3, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) by IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) by TIMESITER(0, x1, 0) -> c10(IF(zero, 0, x1, 0, x1), CHECK(0)) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1), CHECK(s(0))) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1), CHECK(s(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(0, x1, 0) -> c10(IF(zero, 0, x1, 0, x1), CHECK(0)) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1), CHECK(s(0))) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1), CHECK(s(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(0, x1, 0) -> c10(IF(zero, 0, x1, 0, x1), CHECK(0)) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1), CHECK(s(0))) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1), CHECK(s(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2 ---------------------------------------- (91) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: TIMESITER(0, x1, 0) -> c10(IF(zero, 0, x1, 0, x1), CHECK(0)) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1), CHECK(s(0))) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1), CHECK(s(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1), CHECK(s(0))) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1), CHECK(s(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2 ---------------------------------------- (93) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) by TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(0, x1, s(x2)) -> c10(IF(zero, 0, x1, s(x2), s(plus(x2, x1))), CHECK(0)) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), CHECK(s(0))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(0)))) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(0, x1, s(x2)) -> c10(IF(zero, 0, x1, s(x2), s(plus(x2, x1))), CHECK(0)) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), CHECK(s(0))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(0)))) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(0, x1, s(x2)) -> c10(IF(zero, 0, x1, s(x2), s(plus(x2, x1))), CHECK(0)) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), CHECK(s(0))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(0)))) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2 ---------------------------------------- (97) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: TIMESITER(0, x1, s(x2)) -> c10(IF(zero, 0, x1, s(x2), s(plus(x2, x1))), CHECK(0)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), CHECK(s(0))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(0)))) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), CHECK(s(0))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(0)))) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) by TIMESITER(s(s(s(x0))), z0, 0) -> c10(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0), CHECK(s(s(s(x0))))) TIMESITER(s(s(s(x0))), z1, s(z0)) -> c10(IF(check(s(x0)), s(s(s(x0))), z1, s(z0), s(plus(z0, z1))), CHECK(s(s(s(x0))))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2 ---------------------------------------- (103) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) We considered the (Usable) Rules:none And the Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(CHECK(x_1)) = 0 POL(HALF(x_1)) = 0 POL(IF(x_1, x_2, x_3, x_4, x_5)) = [1] POL(PLUS(x_1, x_2)) = 0 POL(TIMESITER(x_1, x_2, x_3)) = [1] POL(c10(x_1)) = x_1 POL(c10(x_1, x_2)) = x_1 + x_2 POL(c11(x_1)) = x_1 POL(c11(x_1, x_2)) = x_1 + x_2 POL(c15(x_1)) = x_1 POL(c16(x_1, x_2)) = x_1 + x_2 POL(c16(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(c17(x_1, x_2)) = x_1 + x_2 POL(c17(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(c18(x_1, x_2)) = x_1 + x_2 POL(c18(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(c19(x_1, x_2)) = x_1 + x_2 POL(c19(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(c3(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(check(x_1)) = 0 POL(even) = [1] POL(half(x_1)) = 0 POL(if(x_1, x_2, x_3, x_4, x_5)) = [1] + x_3 POL(odd) = [1] POL(p(x_1)) = [1] + x_1 POL(plus(x_1, x_2)) = 0 POL(s(x_1)) = 0 POL(timesIter(x_1, x_2, x_3)) = x_2 POL(zero) = [1] ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) by TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(0, x1, s(x2)) -> c11(IF(zero, 0, x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(0, x1, s(x2)) -> c11(IF(zero, 0, x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(0, x1, s(x2)) -> c11(IF(zero, 0, x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2 ---------------------------------------- (109) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) We considered the (Usable) Rules:none And the Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(CHECK(x_1)) = 0 POL(HALF(x_1)) = 0 POL(IF(x_1, x_2, x_3, x_4, x_5)) = [1] POL(PLUS(x_1, x_2)) = 0 POL(TIMESITER(x_1, x_2, x_3)) = [1] POL(c10(x_1)) = x_1 POL(c10(x_1, x_2)) = x_1 + x_2 POL(c11(x_1)) = x_1 POL(c11(x_1, x_2)) = x_1 + x_2 POL(c15(x_1)) = x_1 POL(c16(x_1, x_2)) = x_1 + x_2 POL(c16(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(c17(x_1, x_2)) = x_1 + x_2 POL(c17(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(c18(x_1, x_2)) = x_1 + x_2 POL(c18(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(c19(x_1, x_2)) = x_1 + x_2 POL(c19(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(c3(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(check(x_1)) = 0 POL(even) = [1] POL(half(x_1)) = 0 POL(if(x_1, x_2, x_3, x_4, x_5)) = [1] + x_3 POL(odd) = [1] POL(p(x_1)) = [1] + x_1 POL(plus(x_1, x_2)) = 0 POL(s(x_1)) = 0 POL(timesIter(x_1, x_2, x_3)) = x_2 POL(zero) = [1] ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2 ---------------------------------------- (111) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) by TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0), PLUS(0, z0)) TIMESITER(s(s(s(x0))), z1, s(z0)) -> c11(IF(check(s(x0)), s(s(s(x0))), z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0), PLUS(0, z0)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0), PLUS(0, z0)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2 ---------------------------------------- (115) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) by TIMESITER(0, x1, 0) -> c11(IF(zero, 0, x1, 0, x1)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(s(s(s(z0))), x1, 0) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1)) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(0, x1, 0) -> c11(IF(zero, 0, x1, 0, x1)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(0, x1, 0) -> c11(IF(zero, 0, x1, 0, x1)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2 ---------------------------------------- (117) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: TIMESITER(0, x1, 0) -> c11(IF(zero, 0, x1, 0, x1)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2 ---------------------------------------- (119) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) by IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2 ---------------------------------------- (121) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2 ---------------------------------------- (123) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) by IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(0)), HALF(0)) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(0)), HALF(0)) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(0)), HALF(0)) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(0)), HALF(0)) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(0)), HALF(0)) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(0)), HALF(0)) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2 ---------------------------------------- (125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(0))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(0))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2 ---------------------------------------- (127) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1 ---------------------------------------- (129) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) by IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1 ---------------------------------------- (133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1 ---------------------------------------- (135) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) by IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(z0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, half(s(z0))), timesIter(s(half(x0)), x1, s(half(z0)))), TIMESITER(half(s(s(x0))), x1, half(s(z0))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) by IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(z0)), plus(half(s(z0)), x1)), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) by IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, 0), if(check(half(x0)), half(x0), z1, half(s(0)), plus(half(s(0)), z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(0)), HALF(0)) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, 0), timesIter(s(half(z0)), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(0)), HALF(0)) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(0)), HALF(0)) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(0)), HALF(0)) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(0)), HALF(0)) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(0)), HALF(0)) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1 ---------------------------------------- (145) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1, c1_1 ---------------------------------------- (147) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1, c1_1 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) by IF(even, x0, z1, s(0), x2) -> c16(PLUS(timesIter(half(x0), z1, 0), if(check(half(x0)), half(x0), z1, half(s(s(0))), plus(half(s(s(0))), z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, 0), timesIter(s(half(z0)), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1, c1_1, c16_1 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1, c1_1, c16_1 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) by IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(x0), z1, s(half(x2))), if(check(half(x0)), half(x0), z1, half(s(s(s(x2)))), plus(half(s(s(s(x2)))), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(x2))), timesIter(half(x0), x1, s(half(s(x2))))), TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(x0)) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0)) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, s(half(x2))), timesIter(s(half(z0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0)) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0)) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0)) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0)) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0)) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1, c1_1, c16_1 ---------------------------------------- (155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1, c1_1, c16_1 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) by IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(s(half(x0)), z1, half(x2)), if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(z0), x3) -> c16(PLUS(timesIter(s(half(x0)), x1, half(s(z0))), timesIter(half(s(s(x0))), x1, s(half(z0)))), TIMESITER(half(s(s(x0))), x1, half(s(z0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(s(half(x0)), x1, s(half(z0))), timesIter(half(s(s(x0))), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1 ---------------------------------------- (159) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) by IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, s(z0), x2) -> c16(PLUS(timesIter(half(0), x0, half(s(z0))), timesIter(0, x0, s(half(z0)))), TIMESITER(half(0), x0, half(s(z0)))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, s(0), x2) -> c16(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, s(s(z0)), x2) -> c16(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0))))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1 ---------------------------------------- (161) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1, c2_1 ---------------------------------------- (163) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1, c2_1 ---------------------------------------- (165) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) by IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, s(z0), x2) -> c16(PLUS(timesIter(half(s(0)), x0, half(s(z0))), timesIter(0, x0, s(half(z0)))), TIMESITER(half(s(0)), x0, half(s(z0)))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, s(s(z0)), x2) -> c16(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0))))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1, c2_1 ---------------------------------------- (167) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1, c2_1, c4_1 ---------------------------------------- (169) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1, c2_1, c4_1 ---------------------------------------- (171) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) by IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(0, z1, half(x1)), if(check(half(0)), half(0), z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)), TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, s(z0), x2) -> c16(PLUS(timesIter(0, x0, half(s(z0))), timesIter(half(0), x0, s(half(z0)))), TIMESITER(half(0), x0, half(s(z0)))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))), TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, s(0), x2) -> c16(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, s(s(z0)), x2) -> c16(PLUS(timesIter(0, x0, s(half(z0))), timesIter(half(0), x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0))))) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)), TIMESITER(half(0), x0, half(0))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))), TIMESITER(half(0), x0, half(0))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)), TIMESITER(half(0), x0, half(0))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))), TIMESITER(half(0), x0, half(0))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1, c2_1, c4_1 ---------------------------------------- (173) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1, c2_1, c4_1, c5_1 ---------------------------------------- (175) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1, c2_1, c4_1, c5_1 ---------------------------------------- (177) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) by IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(0, z1, half(x1)), if(check(half(s(0))), half(s(0)), z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)), TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, s(z0), x2) -> c16(PLUS(timesIter(0, x0, half(s(z0))), timesIter(half(s(0)), x0, s(half(z0)))), TIMESITER(half(s(0)), x0, half(s(z0)))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, s(0), x2) -> c16(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, s(s(z0)), x2) -> c16(PLUS(timesIter(0, x0, s(half(z0))), timesIter(half(s(0)), x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0))))) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)), TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)), TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1 ---------------------------------------- (179) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1 ---------------------------------------- (181) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1 ---------------------------------------- (183) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) by IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1 ---------------------------------------- (185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1 ---------------------------------------- (187) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) by IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1 ---------------------------------------- (189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1 ---------------------------------------- (191) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) by IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(0), x0, half(0)), HALF(0)) IF(even, 0, x0, s(z0), x2) -> c17(PLUS(timesIter(half(0), x0, half(s(z0))), timesIter(0, x0, s(half(z0)))), TIMESITER(half(0), x0, half(s(z0))), HALF(s(z0))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(0), x0, half(0)), HALF(0)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))), HALF(s(0))) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(0), x0, half(0)), HALF(0)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(0), x0, half(0)), HALF(0)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))), HALF(s(0))) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(0), x0, half(0)), HALF(0)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(0), x0, half(0)), HALF(0)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))), HALF(s(0))) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1 ---------------------------------------- (193) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1 ---------------------------------------- (195) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1 ---------------------------------------- (197) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1 ---------------------------------------- (199) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) by IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(s(0)), x0, half(0)), HALF(0)) IF(even, s(0), x0, s(z0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, half(s(z0))), timesIter(0, x0, s(half(z0)))), TIMESITER(half(s(0)), x0, half(s(z0))), HALF(s(z0))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))), HALF(s(0))) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)), HALF(0)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(s(0)), x0, half(0)), HALF(0)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))), HALF(s(0))) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)), HALF(0)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(s(0)), x0, half(0)), HALF(0)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))), HALF(s(0))) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)), HALF(0)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1 ---------------------------------------- (201) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1 ---------------------------------------- (203) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1 ---------------------------------------- (205) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1 ---------------------------------------- (207) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) by IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(z0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(s(z0))), timesIter(s(half(x0)), x1, s(half(z0)))), TIMESITER(half(s(s(x0))), x1, half(s(z0))), HALF(s(z0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0)) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0)) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0)) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1 ---------------------------------------- (209) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1 ---------------------------------------- (211) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) by IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(z0)), plus(half(s(z0)), x1)), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1 ---------------------------------------- (213) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1 ---------------------------------------- (215) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) by IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(timesIter(half(x0), z1, s(half(x2))), if(check(half(x0)), half(x0), z1, half(s(s(s(x2)))), plus(half(s(s(s(x2)))), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(x2))), timesIter(half(x0), x1, s(half(s(x2))))), TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, s(half(x2))), timesIter(s(half(z0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1 ---------------------------------------- (217) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) by IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(0, z1, half(x1)), if(check(half(0)), half(0), z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)), TIMESITER(half(0), x0, half(0)), HALF(0)) IF(even, 0, x0, s(z0), x2) -> c17(PLUS(timesIter(0, x0, half(s(z0))), timesIter(half(0), x0, s(half(z0)))), TIMESITER(half(0), x0, half(s(z0))), HALF(s(z0))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))), TIMESITER(half(0), x0, half(0)), HALF(0)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))), HALF(s(0))) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(0, x0, s(half(z0))), timesIter(half(0), x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) ---------------------------------------- (218) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)), TIMESITER(half(0), x0, half(0)), HALF(0)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))), TIMESITER(half(0), x0, half(0)), HALF(0)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))), HALF(s(0))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)), TIMESITER(half(0), x0, half(0)), HALF(0)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))), TIMESITER(half(0), x0, half(0)), HALF(0)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))), HALF(s(0))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1 ---------------------------------------- (219) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (220) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)), TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))), TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)), TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))), TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1 ---------------------------------------- (221) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (222) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1, c13_1 ---------------------------------------- (223) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) ---------------------------------------- (224) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1, c13_1 ---------------------------------------- (225) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) by IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(0, z1, half(x1)), if(check(half(s(0))), half(s(0)), z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)), TIMESITER(half(s(0)), x0, half(0)), HALF(0)) IF(even, s(0), x0, s(z0), x2) -> c17(PLUS(timesIter(0, x0, half(s(z0))), timesIter(half(s(0)), x0, s(half(z0)))), TIMESITER(half(s(0)), x0, half(s(z0))), HALF(s(z0))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)), HALF(0)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))), HALF(s(0))) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(0, x0, s(half(z0))), timesIter(half(s(0)), x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) ---------------------------------------- (226) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)), TIMESITER(half(s(0)), x0, half(0)), HALF(0)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)), HALF(0)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))), HALF(s(0))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)), TIMESITER(half(s(0)), x0, half(0)), HALF(0)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)), HALF(0)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))), HALF(s(0))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1, c13_1 ---------------------------------------- (227) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (228) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)), TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)), TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1, c13_1 ---------------------------------------- (229) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (230) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1, c13_1, c14_1 ---------------------------------------- (231) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) ---------------------------------------- (232) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1, c13_1, c14_1 ---------------------------------------- (233) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) by IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(s(half(x0)), z1, half(x2)), if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0)) IF(even, s(s(x0)), x1, s(z0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(s(z0))), timesIter(half(s(s(x0))), x1, s(half(z0)))), TIMESITER(half(s(s(x0))), x1, half(s(z0))), HALF(s(z0))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0)) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(0))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, s(half(z0))), timesIter(half(s(s(x0))), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) ---------------------------------------- (234) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0)) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(0))) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0)) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(0))) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c9_1, c12_1, c13_1, c14_1 ---------------------------------------- (235) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (236) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c9_1, c12_1, c13_1, c14_1 ---------------------------------------- (237) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) by IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(0))) IF(even, s(s(z0)), x1, 0, x2) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(0))) IF(even, s(s(z0)), x1, 0, x2) -> c17(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0))) ---------------------------------------- (238) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(0))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(0))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c9_1, c12_1, c13_1, c14_1 ---------------------------------------- (239) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (240) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c9_1, c12_1, c13_1, c14_1, c20_1 ---------------------------------------- (241) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) ---------------------------------------- (242) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c9_1, c12_1, c13_1, c14_1, c20_1 ---------------------------------------- (243) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) by IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, 0), if(check(half(x0)), half(x0), z1, half(s(0)), plus(half(s(0)), z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0))) IF(even, s(s(z0)), x1, 0, x2) -> c17(PLUS(timesIter(half(s(s(z0))), x1, 0), timesIter(s(half(z0)), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0))) IF(even, s(s(z0)), x1, 0, x2) -> c17(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0))) ---------------------------------------- (244) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c9_1, c12_1, c13_1, c14_1, c20_1 ---------------------------------------- (245) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (246) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1 ---------------------------------------- (247) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) ---------------------------------------- (248) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1 ---------------------------------------- (249) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) by IF(even, x0, z1, s(0), x2) -> c17(PLUS(timesIter(half(x0), z1, 0), if(check(half(x0)), half(x0), z1, half(s(s(0))), plus(half(s(s(0))), z1))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c17(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, s(s(z0)), x1, s(0), x2) -> c17(PLUS(timesIter(half(s(s(z0))), x1, 0), timesIter(s(half(z0)), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0)))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c17(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c17(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, s(s(z0)), x1, s(0), x2) -> c17(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) ---------------------------------------- (250) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1 ---------------------------------------- (251) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) by IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) ---------------------------------------- (252) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1 ---------------------------------------- (253) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (254) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1 ---------------------------------------- (255) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) by IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) ---------------------------------------- (256) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1 ---------------------------------------- (257) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (258) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(s(0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1 ---------------------------------------- (259) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (260) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1 ---------------------------------------- (261) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) ---------------------------------------- (262) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1 ---------------------------------------- (263) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) by IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0)) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0))) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0)) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0))) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) ---------------------------------------- (264) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0)) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0))) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0)) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0))) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0)) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0))) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0)) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0))) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1 ---------------------------------------- (265) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (266) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1 ---------------------------------------- (267) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) by IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(z0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, half(s(z0))), timesIter(s(half(x0)), x1, s(half(z0)))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) ---------------------------------------- (268) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1 ---------------------------------------- (269) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) by IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(z0)), plus(half(s(z0)), x1)), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) ---------------------------------------- (270) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0)) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1 ---------------------------------------- (271) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (272) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1 ---------------------------------------- (273) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) by IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, 0), if(check(half(x0)), half(x0), z1, half(s(0)), plus(half(s(0)), z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, 0), timesIter(s(half(z0)), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) ---------------------------------------- (274) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0))), HALF(0)) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0))) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1 ---------------------------------------- (275) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (276) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0)))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1 ---------------------------------------- (277) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (278) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c23(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c23(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c23(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c23(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1, c23_1 ---------------------------------------- (279) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c23(TIMESITER(half(0), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c23(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c23(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c23(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) ---------------------------------------- (280) Obligation: Complexity Dependency Tuples Problem Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(z0)))) -> check(s(z0)) plus(0, z0) -> z0 plus(s(z0), z1) -> s(plus(z0, z1)) timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) half(0) -> 0 half(s(0)) -> 0 half(s(s(z0))) -> s(half(z0)) if(zero, z0, z1, z2, z3) -> z2 if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) p(s(z0)) -> z0 p(0) -> 0 Tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c23(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c23(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) S tuples: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) HALF(s(s(z0))) -> c6(HALF(z0)) PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1))) TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1))) TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0)))) TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1)) TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0)) TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0))))) TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1)))) TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0))))) TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0)))))) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0))))))) TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0)) TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1)) TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1)) TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0)) TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1)) TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0)))) IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0)))) IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0))))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0)))))) IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1))) IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1))) IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1))) IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0))))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2))) IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2))) IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0)))) IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0))))) IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0)))))) IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2)))) IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1)) IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0)))) IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1)) IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0)))) IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2)) IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2)) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2)) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0))) IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0)))) IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0))) IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0)))) IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0)) IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0)))) IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2))))) IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0)))))) IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0)))) IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0))))) IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0)))) IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0)) IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0)) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2)))) IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2)))) IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0)) IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0)))) K tuples: TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1)) TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0))))) TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1)) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0))) IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0))) IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0))))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0))) IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0))) IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0))))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0))) IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0))) IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0))))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0))) IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0))) IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0))) IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0))) IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, 0, x1, 0, x2) -> c23(TIMESITER(half(0), x1, half(s(0)))) IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c23(TIMESITER(half(s(0)), x1, half(s(0)))) IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0))))) IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0))))) Defined Rule Symbols: check_1, plus_2, timesIter_3, half_1, if_5, p_1 Defined Pair Symbols: CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3 Compound Symbols: c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1, c23_1