KILLED proof of input_IzQ72M6MWF.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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) CpxTrsToCdtProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (10) TRS for Loop Detection (11) RenamingProof [BOTH BOUNDS(ID, ID), 1 ms] (12) CpxRelTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (18) CdtProblem (19) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (20) CdtProblem (21) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CdtProblem (23) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CdtProblem (25) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CpxRelTRS (27) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (28) CpxTRS (29) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxWeightedTrs (31) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CpxTypedWeightedTrs (33) CompletionProof [UPPER BOUND(ID), 0 ms] (34) CpxTypedWeightedCompleteTrs (35) NarrowingProof [BOTH BOUNDS(ID, ID), 1797 ms] (36) CpxTypedWeightedCompleteTrs (37) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 10 ms] (38) CpxRNTS (39) SimplificationProof [BOTH BOUNDS(ID, ID), 7 ms] (40) CpxRNTS (41) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CpxRNTS (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 129 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 74 ms] (48) CpxRNTS (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (50) CpxRNTS (51) IntTrsBoundProof [UPPER BOUND(ID), 99 ms] (52) CpxRNTS (53) IntTrsBoundProof [UPPER BOUND(ID), 54 ms] (54) CpxRNTS (55) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (56) CpxRNTS (57) IntTrsBoundProof [UPPER BOUND(ID), 292 ms] (58) CpxRNTS (59) IntTrsBoundProof [UPPER BOUND(ID), 54 ms] (60) CpxRNTS (61) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (62) CpxRNTS (63) IntTrsBoundProof [UPPER BOUND(ID), 137 ms] (64) CpxRNTS (65) IntTrsBoundProof [UPPER BOUND(ID), 83 ms] (66) CpxRNTS (67) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (68) CpxRNTS (69) IntTrsBoundProof [UPPER BOUND(ID), 260 ms] (70) CpxRNTS (71) IntTrsBoundProof [UPPER BOUND(ID), 64 ms] (72) CpxRNTS (73) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (74) CpxRNTS (75) IntTrsBoundProof [UPPER BOUND(ID), 340 ms] (76) CpxRNTS (77) IntTrsBoundProof [UPPER BOUND(ID), 33 ms] (78) CpxRNTS (79) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (80) CpxRNTS (81) IntTrsBoundProof [UPPER BOUND(ID), 148 ms] (82) CpxRNTS (83) IntTrsBoundProof [UPPER BOUND(ID), 23 ms] (84) CpxRNTS (85) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (86) CpxRNTS (87) IntTrsBoundProof [UPPER BOUND(ID), 22.8 s] (88) CpxRNTS (89) IntTrsBoundProof [UPPER BOUND(ID), 7909 ms] (90) CpxRNTS (91) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (92) CpxRNTS (93) IntTrsBoundProof [UPPER BOUND(ID), 32.1 s] (94) CpxRNTS (95) IntTrsBoundProof [UPPER BOUND(ID), 15.5 s] (96) CpxRNTS (97) CompletionProof [UPPER BOUND(ID), 30 ms] (98) CpxTypedWeightedCompleteTrs (99) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (100) CpxRNTS (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 91 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (114) CdtProblem (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1 ms] (126) CdtProblem (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (136) CdtProblem (137) CdtLeafRemovalProof [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) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 381 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 326 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (152) CdtProblem (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [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), 16 ms] (172) CdtProblem (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (184) CdtProblem (185) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (186) CdtProblem (187) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (188) CdtProblem (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms] (190) CdtProblem (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (192) CdtProblem (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (194) CdtProblem (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (196) CdtProblem (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (198) CdtProblem (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (200) CdtProblem (201) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (202) CdtProblem (203) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (204) CdtProblem (205) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms] (206) CdtProblem (207) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (208) CdtProblem (209) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (210) CdtProblem (211) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (212) CdtProblem (213) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (214) CdtProblem (215) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (216) CdtProblem (217) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (218) CdtProblem (219) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (220) CdtProblem (221) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (222) CdtProblem (223) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms] (224) CdtProblem (225) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (226) CdtProblem (227) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (228) CdtProblem (229) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (230) CdtProblem (231) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (232) CdtProblem (233) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (234) CdtProblem (235) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 5 ms] (236) CdtProblem (237) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (238) CdtProblem (239) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms] (240) CdtProblem (241) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms] (242) CdtProblem (243) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (244) CdtProblem (245) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (246) CdtProblem (247) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 19 ms] (248) CdtProblem (249) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (250) CdtProblem (251) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (252) CdtProblem (253) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (254) CdtProblem (255) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (256) CdtProblem (257) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms] (258) CdtProblem (259) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 7 ms] (260) CdtProblem (261) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (262) CdtProblem (263) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (264) CdtProblem (265) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (266) CdtProblem (267) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (268) CdtProblem (269) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 13 ms] (270) CdtProblem (271) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (272) CdtProblem (273) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (274) CdtProblem (275) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 3 ms] (276) CdtProblem (277) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (278) CdtProblem (279) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (280) CdtProblem (281) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (282) CdtProblem (283) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms] (284) CdtProblem (285) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 1 ms] (286) CdtProblem (287) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (288) CdtProblem (289) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (290) CdtProblem (291) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (292) CdtProblem (293) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (294) CdtProblem (295) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms] (296) CdtProblem (297) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (298) CdtProblem (299) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (300) CdtProblem (301) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (302) CdtProblem (303) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (304) CdtProblem (305) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (306) CdtProblem (307) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (308) CdtProblem (309) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms] (310) CdtProblem (311) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (312) CdtProblem (313) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (314) CpxWeightedTrs (315) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (316) CpxTypedWeightedTrs (317) CompletionProof [UPPER BOUND(ID), 0 ms] (318) CpxTypedWeightedCompleteTrs (319) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (320) CpxTypedWeightedCompleteTrs (321) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (322) CpxRNTS (323) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (324) CpxRNTS (325) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (326) CpxRNTS (327) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (328) CpxRNTS (329) IntTrsBoundProof [UPPER BOUND(ID), 189 ms] (330) CpxRNTS (331) IntTrsBoundProof [UPPER BOUND(ID), 82 ms] (332) CpxRNTS (333) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (334) CpxRNTS (335) IntTrsBoundProof [UPPER BOUND(ID), 315 ms] (336) CpxRNTS (337) IntTrsBoundProof [UPPER BOUND(ID), 106 ms] (338) CpxRNTS (339) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (340) CpxRNTS (341) IntTrsBoundProof [UPPER BOUND(ID), 252 ms] (342) CpxRNTS (343) IntTrsBoundProof [UPPER BOUND(ID), 45 ms] (344) CpxRNTS (345) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (346) CpxRNTS (347) IntTrsBoundProof [UPPER BOUND(ID), 168 ms] (348) CpxRNTS (349) IntTrsBoundProof [UPPER BOUND(ID), 34 ms] (350) CpxRNTS (351) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (352) CpxRNTS (353) IntTrsBoundProof [UPPER BOUND(ID), 24.2 s] (354) CpxRNTS (355) IntTrsBoundProof [UPPER BOUND(ID), 6730 ms] (356) CpxRNTS (357) CompletionProof [UPPER BOUND(ID), 0 ms] (358) CpxTypedWeightedCompleteTrs (359) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (360) CpxRNTS ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 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) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) 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 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 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))) The (relative) TRS S consists of the following 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)))) Rewrite Strategy: INNERMOST ---------------------------------------- (9) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (10) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 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))) The (relative) TRS S consists of the following 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)))) Rewrite Strategy: INNERMOST ---------------------------------------- (11) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (12) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 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))) The (relative) TRS S consists of the following 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)))) Rewrite Strategy: INNERMOST ---------------------------------------- (13) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (14) Obligation: Innermost TRS: Rules: 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))) 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)))) Types: CHECK :: 0':s -> c:c1:c2:c3 0' :: 0':s c :: c:c1:c2:c3 s :: 0':s -> 0':s c1 :: c:c1:c2:c3 c2 :: c:c1:c2:c3 c3 :: c:c1:c2:c3 -> c:c1:c2:c3 HALF :: 0':s -> c4:c5:c6 c4 :: c4:c5:c6 c5 :: c4:c5:c6 c6 :: c4:c5:c6 -> c4:c5:c6 PLUS :: 0':s -> 0':s -> c7:c8 c7 :: c7:c8 c8 :: c7:c8 -> c7:c8 TIMES :: 0':s -> 0':s -> c9 c9 :: c10:c11 -> c9 TIMESITER :: 0':s -> 0':s -> 0':s -> c10:c11 c10 :: c14:c15:c16:c17:c18:c19 -> c:c1:c2:c3 -> c10:c11 IF :: zero:odd:even -> 0':s -> 0':s -> 0':s -> 0':s -> c14:c15:c16:c17:c18:c19 check :: 0':s -> zero:odd:even plus :: 0':s -> 0':s -> 0':s c11 :: c14:c15:c16:c17:c18:c19 -> c7:c8 -> c10:c11 P :: 0':s -> c12:c13 c12 :: c12:c13 c13 :: c12:c13 zero :: zero:odd:even c14 :: c14:c15:c16:c17:c18:c19 odd :: zero:odd:even c15 :: c10:c11 -> c12:c13 -> c14:c15:c16:c17:c18:c19 p :: 0':s -> 0':s even :: zero:odd:even c16 :: c7:c8 -> c10:c11 -> c4:c5:c6 -> c14:c15:c16:c17:c18:c19 timesIter :: 0':s -> 0':s -> 0':s -> 0':s half :: 0':s -> 0':s c17 :: c7:c8 -> c10:c11 -> c4:c5:c6 -> c14:c15:c16:c17:c18:c19 c18 :: c7:c8 -> c10:c11 -> c4:c5:c6 -> c14:c15:c16:c17:c18:c19 c19 :: c7:c8 -> c10:c11 -> c4:c5:c6 -> c14:c15:c16:c17:c18:c19 times :: 0':s -> 0':s -> 0':s if :: zero:odd:even -> 0':s -> 0':s -> 0':s -> 0':s -> 0':s hole_c:c1:c2:c31_20 :: c:c1:c2:c3 hole_0':s2_20 :: 0':s hole_c4:c5:c63_20 :: c4:c5:c6 hole_c7:c84_20 :: c7:c8 hole_c95_20 :: c9 hole_c10:c116_20 :: c10:c11 hole_c14:c15:c16:c17:c18:c197_20 :: c14:c15:c16:c17:c18:c19 hole_zero:odd:even8_20 :: zero:odd:even hole_c12:c139_20 :: c12:c13 gen_c:c1:c2:c310_20 :: Nat -> c:c1:c2:c3 gen_0':s11_20 :: Nat -> 0':s gen_c4:c5:c612_20 :: Nat -> c4:c5:c6 gen_c7:c813_20 :: Nat -> c7:c8 ---------------------------------------- (15) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: CHECK, HALF, PLUS, TIMESITER, check, plus, timesIter, half They will be analysed ascendingly in the following order: CHECK < TIMESITER HALF < TIMESITER PLUS < TIMESITER check < TIMESITER plus < TIMESITER timesIter < TIMESITER half < TIMESITER check < timesIter plus < timesIter half < timesIter ---------------------------------------- (16) Obligation: Innermost TRS: Rules: 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))) 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)))) Types: CHECK :: 0':s -> c:c1:c2:c3 0' :: 0':s c :: c:c1:c2:c3 s :: 0':s -> 0':s c1 :: c:c1:c2:c3 c2 :: c:c1:c2:c3 c3 :: c:c1:c2:c3 -> c:c1:c2:c3 HALF :: 0':s -> c4:c5:c6 c4 :: c4:c5:c6 c5 :: c4:c5:c6 c6 :: c4:c5:c6 -> c4:c5:c6 PLUS :: 0':s -> 0':s -> c7:c8 c7 :: c7:c8 c8 :: c7:c8 -> c7:c8 TIMES :: 0':s -> 0':s -> c9 c9 :: c10:c11 -> c9 TIMESITER :: 0':s -> 0':s -> 0':s -> c10:c11 c10 :: c14:c15:c16:c17:c18:c19 -> c:c1:c2:c3 -> c10:c11 IF :: zero:odd:even -> 0':s -> 0':s -> 0':s -> 0':s -> c14:c15:c16:c17:c18:c19 check :: 0':s -> zero:odd:even plus :: 0':s -> 0':s -> 0':s c11 :: c14:c15:c16:c17:c18:c19 -> c7:c8 -> c10:c11 P :: 0':s -> c12:c13 c12 :: c12:c13 c13 :: c12:c13 zero :: zero:odd:even c14 :: c14:c15:c16:c17:c18:c19 odd :: zero:odd:even c15 :: c10:c11 -> c12:c13 -> c14:c15:c16:c17:c18:c19 p :: 0':s -> 0':s even :: zero:odd:even c16 :: c7:c8 -> c10:c11 -> c4:c5:c6 -> c14:c15:c16:c17:c18:c19 timesIter :: 0':s -> 0':s -> 0':s -> 0':s half :: 0':s -> 0':s c17 :: c7:c8 -> c10:c11 -> c4:c5:c6 -> c14:c15:c16:c17:c18:c19 c18 :: c7:c8 -> c10:c11 -> c4:c5:c6 -> c14:c15:c16:c17:c18:c19 c19 :: c7:c8 -> c10:c11 -> c4:c5:c6 -> c14:c15:c16:c17:c18:c19 times :: 0':s -> 0':s -> 0':s if :: zero:odd:even -> 0':s -> 0':s -> 0':s -> 0':s -> 0':s hole_c:c1:c2:c31_20 :: c:c1:c2:c3 hole_0':s2_20 :: 0':s hole_c4:c5:c63_20 :: c4:c5:c6 hole_c7:c84_20 :: c7:c8 hole_c95_20 :: c9 hole_c10:c116_20 :: c10:c11 hole_c14:c15:c16:c17:c18:c197_20 :: c14:c15:c16:c17:c18:c19 hole_zero:odd:even8_20 :: zero:odd:even hole_c12:c139_20 :: c12:c13 gen_c:c1:c2:c310_20 :: Nat -> c:c1:c2:c3 gen_0':s11_20 :: Nat -> 0':s gen_c4:c5:c612_20 :: Nat -> c4:c5:c6 gen_c7:c813_20 :: Nat -> c7:c8 Generator Equations: gen_c:c1:c2:c310_20(0) <=> c gen_c:c1:c2:c310_20(+(x, 1)) <=> c3(gen_c:c1:c2:c310_20(x)) gen_0':s11_20(0) <=> 0' gen_0':s11_20(+(x, 1)) <=> s(gen_0':s11_20(x)) gen_c4:c5:c612_20(0) <=> c4 gen_c4:c5:c612_20(+(x, 1)) <=> c6(gen_c4:c5:c612_20(x)) gen_c7:c813_20(0) <=> c7 gen_c7:c813_20(+(x, 1)) <=> c8(gen_c7:c813_20(x)) The following defined symbols remain to be analysed: CHECK, HALF, PLUS, TIMESITER, check, plus, timesIter, half They will be analysed ascendingly in the following order: CHECK < TIMESITER HALF < TIMESITER PLUS < TIMESITER check < TIMESITER plus < TIMESITER timesIter < TIMESITER half < TIMESITER check < timesIter plus < timesIter half < timesIter ---------------------------------------- (17) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (18) 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 ---------------------------------------- (19) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: TIMES(z0, z1) -> c9(TIMESITER(z0, z1, 0)) Removed 9 trailing nodes: CHECK(s(s(0))) -> c2 IF(zero, z0, z1, z2, z3) -> c14 HALF(s(0)) -> c5 CHECK(0) -> c CHECK(s(0)) -> c1 P(0) -> c13 PLUS(0, z0) -> c7 P(s(z0)) -> c12 HALF(0) -> c4 ---------------------------------------- (20) 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 ---------------------------------------- (21) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (22) 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 ---------------------------------------- (23) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: times(z0, z1) -> timesIter(z0, z1, 0) ---------------------------------------- (24) 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 ---------------------------------------- (25) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (26) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 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)) The (relative) TRS S consists of the following 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 Rewrite Strategy: INNERMOST ---------------------------------------- (27) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (28) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 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)) 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 S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (29) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (30) 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(s(s(s(z0)))) -> c3(CHECK(s(z0))) [1] HALF(s(s(z0))) -> c6(HALF(z0)) [1] PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) [1] TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0)) [1] TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) [1] 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)) [1] 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)) [1] 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)) [1] 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))) [1] IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) [1] check(0) -> zero [0] check(s(0)) -> odd [0] check(s(s(0))) -> even [0] check(s(s(s(z0)))) -> check(s(z0)) [0] plus(0, z0) -> z0 [0] plus(s(z0), z1) -> s(plus(z0, z1)) [0] timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) [0] half(0) -> 0 [0] half(s(0)) -> 0 [0] half(s(s(z0))) -> s(half(z0)) [0] if(zero, z0, z1, z2, z3) -> z2 [0] if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) [0] if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) [0] p(s(z0)) -> z0 [0] p(0) -> 0 [0] Rewrite Strategy: INNERMOST ---------------------------------------- (31) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (32) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) [1] HALF(s(s(z0))) -> c6(HALF(z0)) [1] PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) [1] TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0)) [1] TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) [1] 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)) [1] 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)) [1] 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)) [1] 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))) [1] IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) [1] check(0) -> zero [0] check(s(0)) -> odd [0] check(s(s(0))) -> even [0] check(s(s(s(z0)))) -> check(s(z0)) [0] plus(0, z0) -> z0 [0] plus(s(z0), z1) -> s(plus(z0, z1)) [0] timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) [0] half(0) -> 0 [0] half(s(0)) -> 0 [0] half(s(s(z0))) -> s(half(z0)) [0] if(zero, z0, z1, z2, z3) -> z2 [0] if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) [0] if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) [0] p(s(z0)) -> z0 [0] p(0) -> 0 [0] The TRS has the following type information: CHECK :: s:0 -> c3 s :: s:0 -> s:0 c3 :: c3 -> c3 HALF :: s:0 -> c6 c6 :: c6 -> c6 PLUS :: s:0 -> s:0 -> c8 c8 :: c8 -> c8 TIMESITER :: s:0 -> s:0 -> s:0 -> c10:c11 c10 :: c16:c17:c18:c19:c15 -> c3 -> c10:c11 IF :: even:odd:zero -> s:0 -> s:0 -> s:0 -> s:0 -> c16:c17:c18:c19:c15 check :: s:0 -> even:odd:zero plus :: s:0 -> s:0 -> s:0 c11 :: c16:c17:c18:c19:c15 -> c8 -> c10:c11 even :: even:odd:zero c16 :: c8 -> c10:c11 -> c6 -> c16:c17:c18:c19:c15 timesIter :: s:0 -> s:0 -> s:0 -> s:0 half :: s:0 -> s:0 c17 :: c8 -> c10:c11 -> c6 -> c16:c17:c18:c19:c15 c18 :: c8 -> c10:c11 -> c6 -> c16:c17:c18:c19:c15 c19 :: c8 -> c10:c11 -> c6 -> c16:c17:c18:c19:c15 odd :: even:odd:zero c15 :: c10:c11 -> c16:c17:c18:c19:c15 p :: s:0 -> s:0 0 :: s:0 zero :: even:odd:zero if :: even:odd:zero -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 Rewrite Strategy: INNERMOST ---------------------------------------- (33) 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: CHECK_1 HALF_1 PLUS_2 TIMESITER_3 IF_5 (c) The following functions are completely defined: check_1 plus_2 timesIter_3 half_1 if_5 p_1 Due to the following rules being added: check(v0) -> null_check [0] plus(v0, v1) -> 0 [0] timesIter(v0, v1, v2) -> 0 [0] half(v0) -> 0 [0] if(v0, v1, v2, v3, v4) -> 0 [0] p(v0) -> 0 [0] And the following fresh constants: null_check, const, const1, const2, const3, const4 ---------------------------------------- (34) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0))) [1] HALF(s(s(z0))) -> c6(HALF(z0)) [1] PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) [1] TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0)) [1] TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) [1] 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)) [1] 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)) [1] 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)) [1] 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))) [1] IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) [1] check(0) -> zero [0] check(s(0)) -> odd [0] check(s(s(0))) -> even [0] check(s(s(s(z0)))) -> check(s(z0)) [0] plus(0, z0) -> z0 [0] plus(s(z0), z1) -> s(plus(z0, z1)) [0] timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) [0] half(0) -> 0 [0] half(s(0)) -> 0 [0] half(s(s(z0))) -> s(half(z0)) [0] if(zero, z0, z1, z2, z3) -> z2 [0] if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) [0] if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) [0] p(s(z0)) -> z0 [0] p(0) -> 0 [0] check(v0) -> null_check [0] plus(v0, v1) -> 0 [0] timesIter(v0, v1, v2) -> 0 [0] half(v0) -> 0 [0] if(v0, v1, v2, v3, v4) -> 0 [0] p(v0) -> 0 [0] The TRS has the following type information: CHECK :: s:0 -> c3 s :: s:0 -> s:0 c3 :: c3 -> c3 HALF :: s:0 -> c6 c6 :: c6 -> c6 PLUS :: s:0 -> s:0 -> c8 c8 :: c8 -> c8 TIMESITER :: s:0 -> s:0 -> s:0 -> c10:c11 c10 :: c16:c17:c18:c19:c15 -> c3 -> c10:c11 IF :: even:odd:zero:null_check -> s:0 -> s:0 -> s:0 -> s:0 -> c16:c17:c18:c19:c15 check :: s:0 -> even:odd:zero:null_check plus :: s:0 -> s:0 -> s:0 c11 :: c16:c17:c18:c19:c15 -> c8 -> c10:c11 even :: even:odd:zero:null_check c16 :: c8 -> c10:c11 -> c6 -> c16:c17:c18:c19:c15 timesIter :: s:0 -> s:0 -> s:0 -> s:0 half :: s:0 -> s:0 c17 :: c8 -> c10:c11 -> c6 -> c16:c17:c18:c19:c15 c18 :: c8 -> c10:c11 -> c6 -> c16:c17:c18:c19:c15 c19 :: c8 -> c10:c11 -> c6 -> c16:c17:c18:c19:c15 odd :: even:odd:zero:null_check c15 :: c10:c11 -> c16:c17:c18:c19:c15 p :: s:0 -> s:0 0 :: s:0 zero :: even:odd:zero:null_check if :: even:odd:zero:null_check -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 null_check :: even:odd:zero:null_check const :: c3 const1 :: c6 const2 :: c8 const3 :: c10:c11 const4 :: c16:c17:c18:c19:c15 Rewrite Strategy: INNERMOST ---------------------------------------- (35) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (36) 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(s(s(s(z0)))) -> c3(CHECK(s(z0))) [1] HALF(s(s(z0))) -> c6(HALF(z0)) [1] PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) [1] TIMESITER(0, z1, 0) -> c10(IF(zero, 0, z1, 0, z1), CHECK(0)) [1] TIMESITER(0, z1, s(z0'')) -> c10(IF(zero, 0, z1, s(z0''), s(plus(z0'', z1))), CHECK(0)) [1] TIMESITER(0, z1, z2) -> c10(IF(zero, 0, z1, z2, 0), CHECK(0)) [1] TIMESITER(s(0), z1, 0) -> c10(IF(odd, s(0), z1, 0, z1), CHECK(s(0))) [1] TIMESITER(s(0), z1, s(z01)) -> c10(IF(odd, s(0), z1, s(z01), s(plus(z01, z1))), CHECK(s(0))) [1] TIMESITER(s(0), z1, z2) -> c10(IF(odd, s(0), z1, z2, 0), CHECK(s(0))) [1] TIMESITER(s(s(0)), z1, 0) -> c10(IF(even, s(s(0)), z1, 0, z1), CHECK(s(s(0)))) [1] TIMESITER(s(s(0)), z1, s(z02)) -> c10(IF(even, s(s(0)), z1, s(z02), s(plus(z02, z1))), CHECK(s(s(0)))) [1] TIMESITER(s(s(0)), z1, z2) -> c10(IF(even, s(s(0)), z1, z2, 0), CHECK(s(s(0)))) [1] TIMESITER(s(s(s(z0'))), z1, 0) -> c10(IF(check(s(z0')), s(s(s(z0'))), z1, 0, z1), CHECK(s(s(s(z0'))))) [1] TIMESITER(s(s(s(z0'))), z1, s(z03)) -> c10(IF(check(s(z0')), s(s(s(z0'))), z1, s(z03), s(plus(z03, z1))), CHECK(s(s(s(z0'))))) [1] TIMESITER(s(s(s(z0'))), z1, z2) -> c10(IF(check(s(z0')), s(s(s(z0'))), z1, z2, 0), CHECK(s(s(s(z0'))))) [1] TIMESITER(z0, z1, 0) -> c10(IF(null_check, z0, z1, 0, z1), CHECK(z0)) [1] TIMESITER(z0, z1, s(z04)) -> c10(IF(null_check, z0, z1, s(z04), s(plus(z04, z1))), CHECK(z0)) [1] TIMESITER(z0, z1, z2) -> c10(IF(null_check, z0, z1, z2, 0), CHECK(z0)) [1] TIMESITER(0, z1, 0) -> c11(IF(zero, 0, z1, 0, z1), PLUS(0, z1)) [1] TIMESITER(0, z1, s(z06)) -> c11(IF(zero, 0, z1, s(z06), s(plus(z06, z1))), PLUS(s(z06), z1)) [1] TIMESITER(0, z1, z2) -> c11(IF(zero, 0, z1, z2, 0), PLUS(z2, z1)) [1] TIMESITER(s(0), z1, 0) -> c11(IF(odd, s(0), z1, 0, z1), PLUS(0, z1)) [1] TIMESITER(s(0), z1, s(z07)) -> c11(IF(odd, s(0), z1, s(z07), s(plus(z07, z1))), PLUS(s(z07), z1)) [1] TIMESITER(s(0), z1, z2) -> c11(IF(odd, s(0), z1, z2, 0), PLUS(z2, z1)) [1] TIMESITER(s(s(0)), z1, 0) -> c11(IF(even, s(s(0)), z1, 0, z1), PLUS(0, z1)) [1] TIMESITER(s(s(0)), z1, s(z08)) -> c11(IF(even, s(s(0)), z1, s(z08), s(plus(z08, z1))), PLUS(s(z08), z1)) [1] TIMESITER(s(s(0)), z1, z2) -> c11(IF(even, s(s(0)), z1, z2, 0), PLUS(z2, z1)) [1] TIMESITER(s(s(s(z05))), z1, 0) -> c11(IF(check(s(z05)), s(s(s(z05))), z1, 0, z1), PLUS(0, z1)) [1] TIMESITER(s(s(s(z05))), z1, s(z09)) -> c11(IF(check(s(z05)), s(s(s(z05))), z1, s(z09), s(plus(z09, z1))), PLUS(s(z09), z1)) [1] TIMESITER(s(s(s(z05))), z1, z2) -> c11(IF(check(s(z05)), s(s(s(z05))), z1, z2, 0), PLUS(z2, z1)) [1] TIMESITER(z0, z1, 0) -> c11(IF(null_check, z0, z1, 0, z1), PLUS(0, z1)) [1] TIMESITER(z0, z1, s(z010)) -> c11(IF(null_check, z0, z1, s(z010), s(plus(z010, z1))), PLUS(s(z010), z1)) [1] TIMESITER(z0, z1, z2) -> c11(IF(null_check, z0, z1, z2, 0), PLUS(z2, z1)) [1] 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)) [1] 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)) [1] 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)) [1] 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))) [1] IF(odd, s(z0255), z1, z2, z3) -> c15(TIMESITER(z0255, z1, z3)) [1] IF(odd, 0, z1, z2, z3) -> c15(TIMESITER(0, z1, z3)) [1] IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(0, z1, z3)) [1] check(0) -> zero [0] check(s(0)) -> odd [0] check(s(s(0))) -> even [0] check(s(s(s(z0)))) -> check(s(z0)) [0] plus(0, z0) -> z0 [0] plus(s(z0), z1) -> s(plus(z0, z1)) [0] timesIter(0, z1, 0) -> if(zero, 0, z1, 0, z1) [0] timesIter(0, z1, s(z0257)) -> if(zero, 0, z1, s(z0257), s(plus(z0257, z1))) [0] timesIter(0, z1, z2) -> if(zero, 0, z1, z2, 0) [0] timesIter(s(0), z1, 0) -> if(odd, s(0), z1, 0, z1) [0] timesIter(s(0), z1, s(z0258)) -> if(odd, s(0), z1, s(z0258), s(plus(z0258, z1))) [0] timesIter(s(0), z1, z2) -> if(odd, s(0), z1, z2, 0) [0] timesIter(s(s(0)), z1, 0) -> if(even, s(s(0)), z1, 0, z1) [0] timesIter(s(s(0)), z1, s(z0259)) -> if(even, s(s(0)), z1, s(z0259), s(plus(z0259, z1))) [0] timesIter(s(s(0)), z1, z2) -> if(even, s(s(0)), z1, z2, 0) [0] timesIter(s(s(s(z0256))), z1, 0) -> if(check(s(z0256)), s(s(s(z0256))), z1, 0, z1) [0] timesIter(s(s(s(z0256))), z1, s(z0260)) -> if(check(s(z0256)), s(s(s(z0256))), z1, s(z0260), s(plus(z0260, z1))) [0] timesIter(s(s(s(z0256))), z1, z2) -> if(check(s(z0256)), s(s(s(z0256))), z1, z2, 0) [0] timesIter(z0, z1, 0) -> if(null_check, z0, z1, 0, z1) [0] timesIter(z0, z1, s(z0261)) -> if(null_check, z0, z1, s(z0261), s(plus(z0261, z1))) [0] timesIter(z0, z1, z2) -> if(null_check, z0, z1, z2, 0) [0] half(0) -> 0 [0] half(s(0)) -> 0 [0] half(s(s(z0))) -> s(half(z0)) [0] if(zero, z0, z1, z2, z3) -> z2 [0] if(odd, s(z0262), z1, z2, z3) -> timesIter(z0262, z1, z3) [0] if(odd, 0, z1, z2, z3) -> timesIter(0, z1, z3) [0] if(odd, z0, z1, z2, z3) -> timesIter(0, z1, z3) [0] if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) [0] p(s(z0)) -> z0 [0] p(0) -> 0 [0] check(v0) -> null_check [0] plus(v0, v1) -> 0 [0] timesIter(v0, v1, v2) -> 0 [0] half(v0) -> 0 [0] if(v0, v1, v2, v3, v4) -> 0 [0] p(v0) -> 0 [0] The TRS has the following type information: CHECK :: s:0 -> c3 s :: s:0 -> s:0 c3 :: c3 -> c3 HALF :: s:0 -> c6 c6 :: c6 -> c6 PLUS :: s:0 -> s:0 -> c8 c8 :: c8 -> c8 TIMESITER :: s:0 -> s:0 -> s:0 -> c10:c11 c10 :: c16:c17:c18:c19:c15 -> c3 -> c10:c11 IF :: even:odd:zero:null_check -> s:0 -> s:0 -> s:0 -> s:0 -> c16:c17:c18:c19:c15 check :: s:0 -> even:odd:zero:null_check plus :: s:0 -> s:0 -> s:0 c11 :: c16:c17:c18:c19:c15 -> c8 -> c10:c11 even :: even:odd:zero:null_check c16 :: c8 -> c10:c11 -> c6 -> c16:c17:c18:c19:c15 timesIter :: s:0 -> s:0 -> s:0 -> s:0 half :: s:0 -> s:0 c17 :: c8 -> c10:c11 -> c6 -> c16:c17:c18:c19:c15 c18 :: c8 -> c10:c11 -> c6 -> c16:c17:c18:c19:c15 c19 :: c8 -> c10:c11 -> c6 -> c16:c17:c18:c19:c15 odd :: even:odd:zero:null_check c15 :: c10:c11 -> c16:c17:c18:c19:c15 p :: s:0 -> s:0 0 :: s:0 zero :: even:odd:zero:null_check if :: even:odd:zero:null_check -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 null_check :: even:odd:zero:null_check const :: c3 const1 :: c6 const2 :: c8 const3 :: c10:c11 const4 :: c16:c17:c18:c19:c15 Rewrite Strategy: INNERMOST ---------------------------------------- (37) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: even => 1 odd => 2 0 => 0 zero => 3 null_check => 0 const => 0 const1 => 0 const2 => 0 const3 => 0 const4 => 0 ---------------------------------------- (38) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ 1 }-> 1 + CHECK(1 + z0) :|: z0 >= 0, z = 1 + (1 + (1 + z0)) HALF(z) -{ 1 }-> 1 + HALF(z0) :|: z0 >= 0, z = 1 + (1 + z0) IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z0255, z1, z3) :|: z = 2, z1 >= 0, z' = 1 + z0255, z5 = z3, z0255 >= 0, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z1, z3) :|: z = 2, z1 >= 0, z5 = z3, z2 >= 0, z3 >= 0, z' = 0, z'' = z1, z4 = z2 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z1, z3) :|: z = 2, z1 >= 0, z0 >= 0, z5 = z3, z' = z0, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(1 + z2))) + TIMESITER(half(z0), z1, half(z2)) + HALF(z0) :|: z1 >= 0, z = 1, z0 >= 0, z5 = z3, z' = z0, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(1 + z2))) + TIMESITER(half(z0), z1, half(z2)) + HALF(z2) :|: z1 >= 0, z = 1, z0 >= 0, z5 = z3, z' = z0, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(1 + z2))) + TIMESITER(half(z0), z1, half(1 + z2)) + HALF(z0) :|: z1 >= 0, z = 1, z0 >= 0, z5 = z3, z' = z0, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(1 + z2))) + TIMESITER(half(z0), z1, half(1 + z2)) + HALF(1 + z2) :|: z1 >= 0, z = 1, z0 >= 0, z5 = z3, z' = z0, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 PLUS(z, z') -{ 1 }-> 1 + PLUS(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + z0'), 1 + (1 + (1 + z0')), z1, z2, 0) + CHECK(1 + (1 + (1 + z0'))) :|: z'' = z2, z1 >= 0, z0' >= 0, z' = z1, z = 1 + (1 + (1 + z0')), z2 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + z0'), 1 + (1 + (1 + z0')), z1, 0, z1) + CHECK(1 + (1 + (1 + z0'))) :|: z'' = 0, z1 >= 0, z0' >= 0, z' = z1, z = 1 + (1 + (1 + z0')) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + z0'), 1 + (1 + (1 + z0')), z1, 1 + z03, 1 + plus(z03, z1)) + CHECK(1 + (1 + (1 + z0'))) :|: z'' = 1 + z03, z1 >= 0, z0' >= 0, z' = z1, z = 1 + (1 + (1 + z0')), z03 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + z05), 1 + (1 + (1 + z05)), z1, z2, 0) + PLUS(z2, z1) :|: z = 1 + (1 + (1 + z05)), z'' = z2, z1 >= 0, z' = z1, z05 >= 0, z2 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + z05), 1 + (1 + (1 + z05)), z1, 0, z1) + PLUS(0, z1) :|: z'' = 0, z = 1 + (1 + (1 + z05)), z1 >= 0, z' = z1, z05 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + z05), 1 + (1 + (1 + z05)), z1, 1 + z09, 1 + plus(z09, z1)) + PLUS(1 + z09, z1) :|: z = 1 + (1 + (1 + z05)), z1 >= 0, z'' = 1 + z09, z' = z1, z09 >= 0, z05 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z1, z2, 0) + PLUS(z2, z1) :|: z'' = z2, z1 >= 0, z' = z1, z = 0, z2 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z1, z2, 0) + CHECK(0) :|: z'' = z2, z1 >= 0, z' = z1, z = 0, z2 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z1, 0, z1) + PLUS(0, z1) :|: z'' = 0, z1 >= 0, z' = z1, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z1, 0, z1) + CHECK(0) :|: z'' = 0, z1 >= 0, z' = z1, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z1, 1 + z0'', 1 + plus(z0'', z1)) + CHECK(0) :|: z1 >= 0, z'' = 1 + z0'', z' = z1, z0'' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z1, 1 + z06, 1 + plus(z06, z1)) + PLUS(1 + z06, z1) :|: z'' = 1 + z06, z1 >= 0, z06 >= 0, z' = z1, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z1, z2, 0) + PLUS(z2, z1) :|: z'' = z2, z1 >= 0, z = 1 + 0, z' = z1, z2 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z1, z2, 0) + CHECK(1 + 0) :|: z'' = z2, z1 >= 0, z = 1 + 0, z' = z1, z2 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z1, 0, z1) + PLUS(0, z1) :|: z'' = 0, z1 >= 0, z = 1 + 0, z' = z1 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z1, 0, z1) + CHECK(1 + 0) :|: z'' = 0, z1 >= 0, z = 1 + 0, z' = z1 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z1, 1 + z01, 1 + plus(z01, z1)) + CHECK(1 + 0) :|: z1 >= 0, z01 >= 0, z = 1 + 0, z' = z1, z'' = 1 + z01 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z1, 1 + z07, 1 + plus(z07, z1)) + PLUS(1 + z07, z1) :|: z1 >= 0, z07 >= 0, z = 1 + 0, z'' = 1 + z07, z' = z1 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z1, z2, 0) + PLUS(z2, z1) :|: z'' = z2, z1 >= 0, z = 1 + (1 + 0), z' = z1, z2 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z1, z2, 0) + CHECK(1 + (1 + 0)) :|: z'' = z2, z1 >= 0, z = 1 + (1 + 0), z' = z1, z2 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z1, 0, z1) + PLUS(0, z1) :|: z'' = 0, z1 >= 0, z = 1 + (1 + 0), z' = z1 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z1, 0, z1) + CHECK(1 + (1 + 0)) :|: z'' = 0, z1 >= 0, z = 1 + (1 + 0), z' = z1 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z1, 1 + z02, 1 + plus(z02, z1)) + CHECK(1 + (1 + 0)) :|: z1 >= 0, z02 >= 0, z = 1 + (1 + 0), z' = z1, z'' = 1 + z02 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z1, 1 + z08, 1 + plus(z08, z1)) + PLUS(1 + z08, z1) :|: z08 >= 0, z1 >= 0, z'' = 1 + z08, z = 1 + (1 + 0), z' = z1 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z0, z1, z2, 0) + PLUS(z2, z1) :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z0, z1, z2, 0) + CHECK(z0) :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z0, z1, 0, z1) + PLUS(0, z1) :|: z'' = 0, z = z0, z1 >= 0, z' = z1, z0 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z0, z1, 0, z1) + CHECK(z0) :|: z'' = 0, z = z0, z1 >= 0, z' = z1, z0 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z0, z1, 1 + z010, 1 + plus(z010, z1)) + PLUS(1 + z010, z1) :|: z = z0, z1 >= 0, z'' = 1 + z010, z' = z1, z0 >= 0, z010 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z0, z1, 1 + z04, 1 + plus(z04, z1)) + CHECK(z0) :|: z'' = 1 + z04, z04 >= 0, z = z0, z1 >= 0, z' = z1, z0 >= 0 check(z) -{ 0 }-> check(1 + z0) :|: z0 >= 0, z = 1 + (1 + (1 + z0)) check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 half(z) -{ 0 }-> 1 + half(z0) :|: z0 >= 0, z = 1 + (1 + z0) if(z, z', z'', z4, z5) -{ 0 }-> z2 :|: z = 3, z1 >= 0, z0 >= 0, z5 = z3, z' = z0, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z0262, z1, z3) :|: z = 2, z0262 >= 0, z1 >= 0, z' = 1 + z0262, z5 = z3, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z1, z3) :|: z = 2, z1 >= 0, z5 = z3, z2 >= 0, z3 >= 0, z' = 0, z'' = z1, z4 = z2 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z1, z3) :|: z = 2, z1 >= 0, z0 >= 0, z5 = z3, z' = z0, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(1 + z2))) :|: z1 >= 0, z = 1, z0 >= 0, z5 = z3, z' = z0, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z5 = v4, v0 >= 0, v4 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 p(z) -{ 0 }-> z0 :|: z = 1 + z0, z0 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 plus(z, z') -{ 0 }-> z0 :|: z0 >= 0, z = 0, z' = z0 plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 plus(z, z') -{ 0 }-> 1 + plus(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + z0256), 1 + (1 + (1 + z0256)), z1, z2, 0) :|: z0256 >= 0, z'' = z2, z1 >= 0, z' = z1, z = 1 + (1 + (1 + z0256)), z2 >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + z0256), 1 + (1 + (1 + z0256)), z1, 0, z1) :|: z'' = 0, z0256 >= 0, z1 >= 0, z' = z1, z = 1 + (1 + (1 + z0256)) timesIter(z, z', z'') -{ 0 }-> if(check(1 + z0256), 1 + (1 + (1 + z0256)), z1, 1 + z0260, 1 + plus(z0260, z1)) :|: z0256 >= 0, z1 >= 0, z'' = 1 + z0260, z0260 >= 0, z' = z1, z = 1 + (1 + (1 + z0256)) timesIter(z, z', z'') -{ 0 }-> if(3, 0, z1, z2, 0) :|: z'' = z2, z1 >= 0, z' = z1, z = 0, z2 >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z1, 0, z1) :|: z'' = 0, z1 >= 0, z' = z1, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z1, 1 + z0257, 1 + plus(z0257, z1)) :|: z1 >= 0, z0257 >= 0, z' = z1, z'' = 1 + z0257, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z1, z2, 0) :|: z'' = z2, z1 >= 0, z = 1 + 0, z' = z1, z2 >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z1, 0, z1) :|: z'' = 0, z1 >= 0, z = 1 + 0, z' = z1 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z1, 1 + z0258, 1 + plus(z0258, z1)) :|: z1 >= 0, z = 1 + 0, z0258 >= 0, z'' = 1 + z0258, z' = z1 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z1, z2, 0) :|: z'' = z2, z1 >= 0, z = 1 + (1 + 0), z' = z1, z2 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z1, 0, z1) :|: z'' = 0, z1 >= 0, z = 1 + (1 + 0), z' = z1 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z1, 1 + z0259, 1 + plus(z0259, z1)) :|: z1 >= 0, z0259 >= 0, z'' = 1 + z0259, z = 1 + (1 + 0), z' = z1 timesIter(z, z', z'') -{ 0 }-> if(0, z0, z1, z2, 0) :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z0, z1, 0, z1) :|: z'' = 0, z = z0, z1 >= 0, z' = z1, z0 >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z0, z1, 1 + z0261, 1 + plus(z0261, z1)) :|: z = z0, z1 >= 0, z'' = 1 + z0261, z0261 >= 0, z' = z1, z0 >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 ---------------------------------------- (39) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (40) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ 1 }-> 1 + CHECK(1 + (z - 3)) :|: z - 3 >= 0 HALF(z) -{ 1 }-> 1 + HALF(z - 2) :|: z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + HALF(z') :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + HALF(z4) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + HALF(z') :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + HALF(1 + z4) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ 1 }-> 1 + PLUS(z - 1, z') :|: z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + CHECK(1 + (1 + (1 + (z - 3)))) :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + CHECK(1 + (1 + (1 + (z - 3)))) :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + (1 + (1 + (z - 3)))) :|: z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + CHECK(0) :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + CHECK(0) :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(0) :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + CHECK(1 + 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + CHECK(1 + 0) :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + 0) :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + CHECK(1 + (1 + 0)) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + CHECK(1 + (1 + 0)) :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + (1 + 0)) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + CHECK(z) :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + CHECK(z) :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(z) :|: z'' - 1 >= 0, z' >= 0, z >= 0 check(z) -{ 0 }-> check(1 + (z - 3)) :|: z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + half(z - 2) :|: z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') :|: z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 ---------------------------------------- (41) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID)) Found the following analysis order by SCC decomposition: { HALF } { CHECK } { check } { PLUS } { half } { plus } { p } { timesIter, if } { TIMESITER, IF } ---------------------------------------- (42) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ 1 }-> 1 + CHECK(1 + (z - 3)) :|: z - 3 >= 0 HALF(z) -{ 1 }-> 1 + HALF(z - 2) :|: z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + HALF(z') :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + HALF(z4) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + HALF(z') :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + HALF(1 + z4) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ 1 }-> 1 + PLUS(z - 1, z') :|: z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + CHECK(1 + (1 + (1 + (z - 3)))) :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + CHECK(1 + (1 + (1 + (z - 3)))) :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + (1 + (1 + (z - 3)))) :|: z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + CHECK(0) :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + CHECK(0) :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(0) :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + CHECK(1 + 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + CHECK(1 + 0) :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + 0) :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + CHECK(1 + (1 + 0)) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + CHECK(1 + (1 + 0)) :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + (1 + 0)) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + CHECK(z) :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + CHECK(z) :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(z) :|: z'' - 1 >= 0, z' >= 0, z >= 0 check(z) -{ 0 }-> check(1 + (z - 3)) :|: z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + half(z - 2) :|: z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') :|: z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {HALF}, {CHECK}, {check}, {PLUS}, {half}, {plus}, {p}, {timesIter,if}, {TIMESITER,IF} ---------------------------------------- (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 }-> 1 + CHECK(1 + (z - 3)) :|: z - 3 >= 0 HALF(z) -{ 1 }-> 1 + HALF(z - 2) :|: z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + HALF(z') :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + HALF(z4) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + HALF(z') :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + HALF(1 + z4) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ 1 }-> 1 + PLUS(z - 1, z') :|: z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + CHECK(1 + (1 + (1 + (z - 3)))) :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + CHECK(1 + (1 + (1 + (z - 3)))) :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + (1 + (1 + (z - 3)))) :|: z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + CHECK(0) :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + CHECK(0) :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(0) :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + CHECK(1 + 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + CHECK(1 + 0) :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + 0) :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + CHECK(1 + (1 + 0)) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + CHECK(1 + (1 + 0)) :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + (1 + 0)) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + CHECK(z) :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + CHECK(z) :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(z) :|: z'' - 1 >= 0, z' >= 0, z >= 0 check(z) -{ 0 }-> check(1 + (z - 3)) :|: z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + half(z - 2) :|: z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') :|: z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {HALF}, {CHECK}, {check}, {PLUS}, {half}, {plus}, {p}, {timesIter,if}, {TIMESITER,IF} ---------------------------------------- (45) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: HALF after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (46) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ 1 }-> 1 + CHECK(1 + (z - 3)) :|: z - 3 >= 0 HALF(z) -{ 1 }-> 1 + HALF(z - 2) :|: z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + HALF(z') :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + HALF(z4) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + HALF(z') :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + HALF(1 + z4) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ 1 }-> 1 + PLUS(z - 1, z') :|: z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + CHECK(1 + (1 + (1 + (z - 3)))) :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + CHECK(1 + (1 + (1 + (z - 3)))) :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + (1 + (1 + (z - 3)))) :|: z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + CHECK(0) :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + CHECK(0) :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(0) :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + CHECK(1 + 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + CHECK(1 + 0) :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + 0) :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + CHECK(1 + (1 + 0)) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + CHECK(1 + (1 + 0)) :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + (1 + 0)) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + CHECK(z) :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + CHECK(z) :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(z) :|: z'' - 1 >= 0, z' >= 0, z >= 0 check(z) -{ 0 }-> check(1 + (z - 3)) :|: z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + half(z - 2) :|: z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') :|: z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {HALF}, {CHECK}, {check}, {PLUS}, {half}, {plus}, {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: ?, size: O(1) [0] ---------------------------------------- (47) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using KoAT for: HALF after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z ---------------------------------------- (48) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ 1 }-> 1 + CHECK(1 + (z - 3)) :|: z - 3 >= 0 HALF(z) -{ 1 }-> 1 + HALF(z - 2) :|: z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + HALF(z') :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + HALF(z4) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + HALF(z') :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + HALF(1 + z4) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ 1 }-> 1 + PLUS(z - 1, z') :|: z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + CHECK(1 + (1 + (1 + (z - 3)))) :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + CHECK(1 + (1 + (1 + (z - 3)))) :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + (1 + (1 + (z - 3)))) :|: z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + CHECK(0) :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + CHECK(0) :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(0) :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + CHECK(1 + 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + CHECK(1 + 0) :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + 0) :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + CHECK(1 + (1 + 0)) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + CHECK(1 + (1 + 0)) :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + (1 + 0)) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + CHECK(z) :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + CHECK(z) :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(z) :|: z'' - 1 >= 0, z' >= 0, z >= 0 check(z) -{ 0 }-> check(1 + (z - 3)) :|: z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + half(z - 2) :|: z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') :|: z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {CHECK}, {check}, {PLUS}, {half}, {plus}, {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] ---------------------------------------- (49) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (50) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ 1 }-> 1 + CHECK(1 + (z - 3)) :|: z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s' :|: s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s'' :|: s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s1 :|: s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s2 :|: s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ 1 }-> 1 + PLUS(z - 1, z') :|: z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + CHECK(1 + (1 + (1 + (z - 3)))) :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + CHECK(1 + (1 + (1 + (z - 3)))) :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + (1 + (1 + (z - 3)))) :|: z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + CHECK(0) :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + CHECK(0) :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(0) :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + CHECK(1 + 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + CHECK(1 + 0) :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + 0) :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + CHECK(1 + (1 + 0)) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + CHECK(1 + (1 + 0)) :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + (1 + 0)) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + CHECK(z) :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + CHECK(z) :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(z) :|: z'' - 1 >= 0, z' >= 0, z >= 0 check(z) -{ 0 }-> check(1 + (z - 3)) :|: z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + half(z - 2) :|: z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') :|: z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {CHECK}, {check}, {PLUS}, {half}, {plus}, {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] ---------------------------------------- (51) 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: 0 ---------------------------------------- (52) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ 1 }-> 1 + CHECK(1 + (z - 3)) :|: z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s' :|: s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s'' :|: s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s1 :|: s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s2 :|: s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ 1 }-> 1 + PLUS(z - 1, z') :|: z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + CHECK(1 + (1 + (1 + (z - 3)))) :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + CHECK(1 + (1 + (1 + (z - 3)))) :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + (1 + (1 + (z - 3)))) :|: z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + CHECK(0) :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + CHECK(0) :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(0) :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + CHECK(1 + 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + CHECK(1 + 0) :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + 0) :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + CHECK(1 + (1 + 0)) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + CHECK(1 + (1 + 0)) :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + (1 + 0)) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + CHECK(z) :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + CHECK(z) :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(z) :|: z'' - 1 >= 0, z' >= 0, z >= 0 check(z) -{ 0 }-> check(1 + (z - 3)) :|: z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + half(z - 2) :|: z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') :|: z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {CHECK}, {check}, {PLUS}, {half}, {plus}, {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: ?, size: O(1) [0] ---------------------------------------- (53) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using KoAT for: CHECK after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z ---------------------------------------- (54) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ 1 }-> 1 + CHECK(1 + (z - 3)) :|: z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s' :|: s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s'' :|: s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s1 :|: s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s2 :|: s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ 1 }-> 1 + PLUS(z - 1, z') :|: z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + CHECK(1 + (1 + (1 + (z - 3)))) :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + CHECK(1 + (1 + (1 + (z - 3)))) :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + (1 + (1 + (z - 3)))) :|: z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + CHECK(0) :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + CHECK(0) :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(0) :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + CHECK(1 + 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + CHECK(1 + 0) :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + 0) :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + CHECK(1 + (1 + 0)) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + CHECK(1 + (1 + 0)) :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(1 + (1 + 0)) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + CHECK(z) :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + CHECK(z) :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + CHECK(z) :|: z'' - 1 >= 0, z' >= 0, z >= 0 check(z) -{ 0 }-> check(1 + (z - 3)) :|: z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + half(z - 2) :|: z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') :|: z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {check}, {PLUS}, {half}, {plus}, {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] ---------------------------------------- (55) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (56) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s' :|: s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s'' :|: s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s1 :|: s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s2 :|: s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ 1 }-> 1 + PLUS(z - 1, z') :|: z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s14 :|: s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s5 :|: s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s8 :|: s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s11 :|: s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s17 :|: s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> check(1 + (z - 3)) :|: z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + half(z - 2) :|: z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') :|: z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {check}, {PLUS}, {half}, {plus}, {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] ---------------------------------------- (57) 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: 3 ---------------------------------------- (58) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s' :|: s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s'' :|: s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s1 :|: s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s2 :|: s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ 1 }-> 1 + PLUS(z - 1, z') :|: z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s14 :|: s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s5 :|: s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s8 :|: s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s11 :|: s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s17 :|: s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> check(1 + (z - 3)) :|: z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + half(z - 2) :|: z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') :|: z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {check}, {PLUS}, {half}, {plus}, {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: ?, size: O(1) [3] ---------------------------------------- (59) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: check after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (60) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s' :|: s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s'' :|: s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s1 :|: s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s2 :|: s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ 1 }-> 1 + PLUS(z - 1, z') :|: z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s14 :|: s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s5 :|: s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s8 :|: s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s11 :|: s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s17 :|: s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> check(1 + (z - 3)) :|: z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + half(z - 2) :|: z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 0, z') :|: z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(1 + (z - 3)), 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {PLUS}, {half}, {plus}, {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] ---------------------------------------- (61) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (62) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s' :|: s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s'' :|: s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s1 :|: s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s2 :|: s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ 1 }-> 1 + PLUS(z - 1, z') :|: z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s14 :|: s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + PLUS(0, z') :|: s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + PLUS(z'', z') :|: s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s5 :|: s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s8 :|: s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s11 :|: s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s17 :|: s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + half(z - 2) :|: z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s26, 1 + (1 + (1 + (z - 3))), z', 0, z') :|: s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(s27, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s28, 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {PLUS}, {half}, {plus}, {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] ---------------------------------------- (63) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: PLUS after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (64) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s' :|: s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s'' :|: s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s1 :|: s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s2 :|: s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ 1 }-> 1 + PLUS(z - 1, z') :|: z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s14 :|: s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + PLUS(0, z') :|: s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + PLUS(z'', z') :|: s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s5 :|: s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s8 :|: s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s11 :|: s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s17 :|: s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + half(z - 2) :|: z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s26, 1 + (1 + (1 + (z - 3))), z', 0, z') :|: s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(s27, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s28, 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {PLUS}, {half}, {plus}, {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] PLUS: runtime: ?, size: O(1) [0] ---------------------------------------- (65) 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: z ---------------------------------------- (66) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s' :|: s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s'' :|: s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s1 :|: s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s2 :|: s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ 1 }-> 1 + PLUS(z - 1, z') :|: z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s14 :|: s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + PLUS(0, z') :|: s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + PLUS(z'', z') :|: s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s5 :|: s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s8 :|: s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s11 :|: s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', z'', 0) + PLUS(z'', z') :|: z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + PLUS(0, z') :|: z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s17 :|: s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + PLUS(1 + (z'' - 1), z') :|: z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + half(z - 2) :|: z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s26, 1 + (1 + (1 + (z - 3))), z', 0, z') :|: s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(s27, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s28, 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {half}, {plus}, {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] PLUS: runtime: O(n^1) [z], size: O(1) [0] ---------------------------------------- (67) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (68) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s' :|: s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s'' :|: s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s1 :|: s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s2 :|: s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ z }-> 1 + s29 :|: s29 >= 0, s29 <= 0, z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s14 :|: s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + s39 :|: s39 >= 0, s39 <= 0, s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s40 :|: s40 >= 0, s40 <= 0, s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s41 :|: s41 >= 0, s41 <= 0, s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', z'', 0) + s32 :|: s32 >= 0, s32 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s30 :|: s30 >= 0, s30 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s31 :|: s31 >= 0, s31 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s5 :|: s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', z'', 0) + s35 :|: s35 >= 0, s35 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + s33 :|: s33 >= 0, s33 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s34 :|: s34 >= 0, s34 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s8 :|: s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s38 :|: s38 >= 0, s38 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s36 :|: s36 >= 0, s36 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s11 :|: s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s37 :|: s37 >= 0, s37 <= 0, z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', z'', 0) + s44 :|: s44 >= 0, s44 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + s42 :|: s42 >= 0, s42 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s17 :|: s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s43 :|: s43 >= 0, s43 <= 0, z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + half(z - 2) :|: z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s26, 1 + (1 + (1 + (z - 3))), z', 0, z') :|: s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(s27, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s28, 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {half}, {plus}, {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] PLUS: runtime: O(n^1) [z], size: O(1) [0] ---------------------------------------- (69) 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 ---------------------------------------- (70) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s' :|: s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s'' :|: s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s1 :|: s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s2 :|: s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ z }-> 1 + s29 :|: s29 >= 0, s29 <= 0, z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s14 :|: s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + s39 :|: s39 >= 0, s39 <= 0, s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s40 :|: s40 >= 0, s40 <= 0, s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s41 :|: s41 >= 0, s41 <= 0, s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', z'', 0) + s32 :|: s32 >= 0, s32 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s30 :|: s30 >= 0, s30 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s31 :|: s31 >= 0, s31 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s5 :|: s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', z'', 0) + s35 :|: s35 >= 0, s35 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + s33 :|: s33 >= 0, s33 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s34 :|: s34 >= 0, s34 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s8 :|: s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s38 :|: s38 >= 0, s38 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s36 :|: s36 >= 0, s36 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s11 :|: s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s37 :|: s37 >= 0, s37 <= 0, z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', z'', 0) + s44 :|: s44 >= 0, s44 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + s42 :|: s42 >= 0, s42 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s17 :|: s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s43 :|: s43 >= 0, s43 <= 0, z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + half(z - 2) :|: z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s26, 1 + (1 + (1 + (z - 3))), z', 0, z') :|: s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(s27, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s28, 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {half}, {plus}, {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] PLUS: runtime: O(n^1) [z], size: O(1) [0] half: runtime: ?, size: O(n^1) [z] ---------------------------------------- (71) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: half after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (72) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s' :|: s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(z4)) + s'' :|: s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s1 :|: s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) + TIMESITER(half(z'), z'', half(1 + z4)) + s2 :|: s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ z }-> 1 + s29 :|: s29 >= 0, s29 <= 0, z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s14 :|: s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + s39 :|: s39 >= 0, s39 <= 0, s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s40 :|: s40 >= 0, s40 <= 0, s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s41 :|: s41 >= 0, s41 <= 0, s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', z'', 0) + s32 :|: s32 >= 0, s32 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s30 :|: s30 >= 0, s30 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s31 :|: s31 >= 0, s31 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s5 :|: s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', z'', 0) + s35 :|: s35 >= 0, s35 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + s33 :|: s33 >= 0, s33 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s34 :|: s34 >= 0, s34 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s8 :|: s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s38 :|: s38 >= 0, s38 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s36 :|: s36 >= 0, s36 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s11 :|: s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s37 :|: s37 >= 0, s37 <= 0, z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', z'', 0) + s44 :|: s44 >= 0, s44 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + s42 :|: s42 >= 0, s42 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s17 :|: s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s43 :|: s43 >= 0, s43 <= 0, z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + half(z - 2) :|: z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z'), z'', half(z4)), timesIter(half(z'), z'', half(1 + z4))) :|: z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s26, 1 + (1 + (1 + (z - 3))), z', 0, z') :|: s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(s27, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s28, 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {plus}, {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] PLUS: runtime: O(n^1) [z], size: O(1) [0] half: runtime: O(1) [0], size: O(n^1) [z] ---------------------------------------- (73) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (74) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s45, z'', s46), timesIter(s47, z'', s48)) + TIMESITER(s49, z'', s50) + s' :|: s45 >= 0, s45 <= z', s46 >= 0, s46 <= z4, s47 >= 0, s47 <= z', s48 >= 0, s48 <= 1 + z4, s49 >= 0, s49 <= z', s50 >= 0, s50 <= z4, s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(s51, z'', s52), timesIter(s53, z'', s54)) + TIMESITER(s55, z'', s56) + s'' :|: s51 >= 0, s51 <= z', s52 >= 0, s52 <= z4, s53 >= 0, s53 <= z', s54 >= 0, s54 <= 1 + z4, s55 >= 0, s55 <= z', s56 >= 0, s56 <= z4, s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s57, z'', s58), timesIter(s59, z'', s60)) + TIMESITER(s61, z'', s62) + s1 :|: s57 >= 0, s57 <= z', s58 >= 0, s58 <= z4, s59 >= 0, s59 <= z', s60 >= 0, s60 <= 1 + z4, s61 >= 0, s61 <= z', s62 >= 0, s62 <= 1 + z4, s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(s63, z'', s64), timesIter(s65, z'', s66)) + TIMESITER(s67, z'', s68) + s2 :|: s63 >= 0, s63 <= z', s64 >= 0, s64 <= z4, s65 >= 0, s65 <= z', s66 >= 0, s66 <= 1 + z4, s67 >= 0, s67 <= z', s68 >= 0, s68 <= 1 + z4, s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ z }-> 1 + s29 :|: s29 >= 0, s29 <= 0, z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s14 :|: s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + s39 :|: s39 >= 0, s39 <= 0, s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s40 :|: s40 >= 0, s40 <= 0, s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s41 :|: s41 >= 0, s41 <= 0, s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', z'', 0) + s32 :|: s32 >= 0, s32 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s30 :|: s30 >= 0, s30 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s31 :|: s31 >= 0, s31 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s5 :|: s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', z'', 0) + s35 :|: s35 >= 0, s35 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + s33 :|: s33 >= 0, s33 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s34 :|: s34 >= 0, s34 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s8 :|: s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s38 :|: s38 >= 0, s38 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s36 :|: s36 >= 0, s36 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s11 :|: s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s37 :|: s37 >= 0, s37 <= 0, z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', z'', 0) + s44 :|: s44 >= 0, s44 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + s42 :|: s42 >= 0, s42 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s17 :|: s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s43 :|: s43 >= 0, s43 <= 0, z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + s69 :|: s69 >= 0, s69 <= z - 2, z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(s70, z'', s71), timesIter(s72, z'', s73)) :|: s70 >= 0, s70 <= z', s71 >= 0, s71 <= z4, s72 >= 0, s72 <= z', s73 >= 0, s73 <= 1 + z4, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s26, 1 + (1 + (1 + (z - 3))), z', 0, z') :|: s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(s27, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s28, 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {plus}, {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] PLUS: runtime: O(n^1) [z], size: O(1) [0] half: runtime: O(1) [0], size: O(n^1) [z] ---------------------------------------- (75) 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' ---------------------------------------- (76) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s45, z'', s46), timesIter(s47, z'', s48)) + TIMESITER(s49, z'', s50) + s' :|: s45 >= 0, s45 <= z', s46 >= 0, s46 <= z4, s47 >= 0, s47 <= z', s48 >= 0, s48 <= 1 + z4, s49 >= 0, s49 <= z', s50 >= 0, s50 <= z4, s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(s51, z'', s52), timesIter(s53, z'', s54)) + TIMESITER(s55, z'', s56) + s'' :|: s51 >= 0, s51 <= z', s52 >= 0, s52 <= z4, s53 >= 0, s53 <= z', s54 >= 0, s54 <= 1 + z4, s55 >= 0, s55 <= z', s56 >= 0, s56 <= z4, s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s57, z'', s58), timesIter(s59, z'', s60)) + TIMESITER(s61, z'', s62) + s1 :|: s57 >= 0, s57 <= z', s58 >= 0, s58 <= z4, s59 >= 0, s59 <= z', s60 >= 0, s60 <= 1 + z4, s61 >= 0, s61 <= z', s62 >= 0, s62 <= 1 + z4, s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(s63, z'', s64), timesIter(s65, z'', s66)) + TIMESITER(s67, z'', s68) + s2 :|: s63 >= 0, s63 <= z', s64 >= 0, s64 <= z4, s65 >= 0, s65 <= z', s66 >= 0, s66 <= 1 + z4, s67 >= 0, s67 <= z', s68 >= 0, s68 <= 1 + z4, s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ z }-> 1 + s29 :|: s29 >= 0, s29 <= 0, z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s14 :|: s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + s39 :|: s39 >= 0, s39 <= 0, s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s40 :|: s40 >= 0, s40 <= 0, s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s41 :|: s41 >= 0, s41 <= 0, s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', z'', 0) + s32 :|: s32 >= 0, s32 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s30 :|: s30 >= 0, s30 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s31 :|: s31 >= 0, s31 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s5 :|: s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', z'', 0) + s35 :|: s35 >= 0, s35 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + s33 :|: s33 >= 0, s33 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s34 :|: s34 >= 0, s34 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s8 :|: s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s38 :|: s38 >= 0, s38 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s36 :|: s36 >= 0, s36 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s11 :|: s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s37 :|: s37 >= 0, s37 <= 0, z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', z'', 0) + s44 :|: s44 >= 0, s44 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + s42 :|: s42 >= 0, s42 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s17 :|: s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s43 :|: s43 >= 0, s43 <= 0, z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + s69 :|: s69 >= 0, s69 <= z - 2, z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(s70, z'', s71), timesIter(s72, z'', s73)) :|: s70 >= 0, s70 <= z', s71 >= 0, s71 <= z4, s72 >= 0, s72 <= z', s73 >= 0, s73 <= 1 + z4, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s26, 1 + (1 + (1 + (z - 3))), z', 0, z') :|: s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(s27, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s28, 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {plus}, {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] PLUS: runtime: O(n^1) [z], size: O(1) [0] half: runtime: O(1) [0], size: O(n^1) [z] plus: runtime: ?, size: O(n^1) [z + z'] ---------------------------------------- (77) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: plus after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (78) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s45, z'', s46), timesIter(s47, z'', s48)) + TIMESITER(s49, z'', s50) + s' :|: s45 >= 0, s45 <= z', s46 >= 0, s46 <= z4, s47 >= 0, s47 <= z', s48 >= 0, s48 <= 1 + z4, s49 >= 0, s49 <= z', s50 >= 0, s50 <= z4, s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(s51, z'', s52), timesIter(s53, z'', s54)) + TIMESITER(s55, z'', s56) + s'' :|: s51 >= 0, s51 <= z', s52 >= 0, s52 <= z4, s53 >= 0, s53 <= z', s54 >= 0, s54 <= 1 + z4, s55 >= 0, s55 <= z', s56 >= 0, s56 <= z4, s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s57, z'', s58), timesIter(s59, z'', s60)) + TIMESITER(s61, z'', s62) + s1 :|: s57 >= 0, s57 <= z', s58 >= 0, s58 <= z4, s59 >= 0, s59 <= z', s60 >= 0, s60 <= 1 + z4, s61 >= 0, s61 <= z', s62 >= 0, s62 <= 1 + z4, s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(s63, z'', s64), timesIter(s65, z'', s66)) + TIMESITER(s67, z'', s68) + s2 :|: s63 >= 0, s63 <= z', s64 >= 0, s64 <= z4, s65 >= 0, s65 <= z', s66 >= 0, s66 <= 1 + z4, s67 >= 0, s67 <= z', s68 >= 0, s68 <= 1 + z4, s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ z }-> 1 + s29 :|: s29 >= 0, s29 <= 0, z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s14 :|: s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + s39 :|: s39 >= 0, s39 <= 0, s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s40 :|: s40 >= 0, s40 <= 0, s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s41 :|: s41 >= 0, s41 <= 0, s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', z'', 0) + s32 :|: s32 >= 0, s32 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s30 :|: s30 >= 0, s30 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s31 :|: s31 >= 0, s31 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s5 :|: s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', z'', 0) + s35 :|: s35 >= 0, s35 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + s33 :|: s33 >= 0, s33 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s34 :|: s34 >= 0, s34 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s8 :|: s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s38 :|: s38 >= 0, s38 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s36 :|: s36 >= 0, s36 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s11 :|: s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s37 :|: s37 >= 0, s37 <= 0, z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', z'', 0) + s44 :|: s44 >= 0, s44 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + s42 :|: s42 >= 0, s42 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s17 :|: s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) + s43 :|: s43 >= 0, s43 <= 0, z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + s69 :|: s69 >= 0, s69 <= z - 2, z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(s70, z'', s71), timesIter(s72, z'', s73)) :|: s70 >= 0, s70 <= z', s71 >= 0, s71 <= z4, s72 >= 0, s72 <= z', s73 >= 0, s73 <= 1 + z4, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + plus(z - 1, z') :|: z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s26, 1 + (1 + (1 + (z - 3))), z', 0, z') :|: s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(s27, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s28, 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + plus(z'' - 1, z')) :|: z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] PLUS: runtime: O(n^1) [z], size: O(1) [0] half: runtime: O(1) [0], size: O(n^1) [z] plus: runtime: O(1) [0], size: O(n^1) [z + z'] ---------------------------------------- (79) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (80) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s45, z'', s46), timesIter(s47, z'', s48)) + TIMESITER(s49, z'', s50) + s' :|: s45 >= 0, s45 <= z', s46 >= 0, s46 <= z4, s47 >= 0, s47 <= z', s48 >= 0, s48 <= 1 + z4, s49 >= 0, s49 <= z', s50 >= 0, s50 <= z4, s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(s51, z'', s52), timesIter(s53, z'', s54)) + TIMESITER(s55, z'', s56) + s'' :|: s51 >= 0, s51 <= z', s52 >= 0, s52 <= z4, s53 >= 0, s53 <= z', s54 >= 0, s54 <= 1 + z4, s55 >= 0, s55 <= z', s56 >= 0, s56 <= z4, s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s57, z'', s58), timesIter(s59, z'', s60)) + TIMESITER(s61, z'', s62) + s1 :|: s57 >= 0, s57 <= z', s58 >= 0, s58 <= z4, s59 >= 0, s59 <= z', s60 >= 0, s60 <= 1 + z4, s61 >= 0, s61 <= z', s62 >= 0, s62 <= 1 + z4, s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(s63, z'', s64), timesIter(s65, z'', s66)) + TIMESITER(s67, z'', s68) + s2 :|: s63 >= 0, s63 <= z', s64 >= 0, s64 <= z4, s65 >= 0, s65 <= z', s66 >= 0, s66 <= 1 + z4, s67 >= 0, s67 <= z', s68 >= 0, s68 <= 1 + z4, s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ z }-> 1 + s29 :|: s29 >= 0, s29 <= 0, z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s77) + s14 :|: s77 >= 0, s77 <= z'' - 1 + z', s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + s39 :|: s39 >= 0, s39 <= 0, s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s82) + s40 :|: s82 >= 0, s82 <= z'' - 1 + z', s40 >= 0, s40 <= 0, s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s41 :|: s41 >= 0, s41 <= 0, s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', z'', 0) + s32 :|: s32 >= 0, s32 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s30 :|: s30 >= 0, s30 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s74) + s5 :|: s74 >= 0, s74 <= z'' - 1 + z', s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s79) + s31 :|: s79 >= 0, s79 <= z'' - 1 + z', s31 >= 0, s31 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', z'', 0) + s35 :|: s35 >= 0, s35 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + s33 :|: s33 >= 0, s33 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s75) + s8 :|: s75 >= 0, s75 <= z'' - 1 + z', s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s80) + s34 :|: s80 >= 0, s80 <= z'' - 1 + z', s34 >= 0, s34 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s38 :|: s38 >= 0, s38 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s36 :|: s36 >= 0, s36 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s76) + s11 :|: s76 >= 0, s76 <= z'' - 1 + z', s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s81) + s37 :|: s81 >= 0, s81 <= z'' - 1 + z', s37 >= 0, s37 <= 0, z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', z'', 0) + s44 :|: s44 >= 0, s44 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + s42 :|: s42 >= 0, s42 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s78) + s17 :|: s78 >= 0, s78 <= z'' - 1 + z', s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s83) + s43 :|: s83 >= 0, s83 <= z'' - 1 + z', s43 >= 0, s43 <= 0, z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + s69 :|: s69 >= 0, s69 <= z - 2, z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(s70, z'', s71), timesIter(s72, z'', s73)) :|: s70 >= 0, s70 <= z', s71 >= 0, s71 <= z4, s72 >= 0, s72 <= z', s73 >= 0, s73 <= 1 + z4, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + s84 :|: s84 >= 0, s84 <= z - 1 + z', z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s26, 1 + (1 + (1 + (z - 3))), z', 0, z') :|: s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(s27, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s88) :|: s88 >= 0, s88 <= z'' - 1 + z', s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s28, 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + s85) :|: s85 >= 0, s85 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + s86) :|: s86 >= 0, s86 <= z'' - 1 + z', z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s87) :|: s87 >= 0, s87 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + s89) :|: s89 >= 0, s89 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] PLUS: runtime: O(n^1) [z], size: O(1) [0] half: runtime: O(1) [0], size: O(n^1) [z] plus: runtime: O(1) [0], size: O(n^1) [z + z'] ---------------------------------------- (81) 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 ---------------------------------------- (82) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s45, z'', s46), timesIter(s47, z'', s48)) + TIMESITER(s49, z'', s50) + s' :|: s45 >= 0, s45 <= z', s46 >= 0, s46 <= z4, s47 >= 0, s47 <= z', s48 >= 0, s48 <= 1 + z4, s49 >= 0, s49 <= z', s50 >= 0, s50 <= z4, s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(s51, z'', s52), timesIter(s53, z'', s54)) + TIMESITER(s55, z'', s56) + s'' :|: s51 >= 0, s51 <= z', s52 >= 0, s52 <= z4, s53 >= 0, s53 <= z', s54 >= 0, s54 <= 1 + z4, s55 >= 0, s55 <= z', s56 >= 0, s56 <= z4, s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s57, z'', s58), timesIter(s59, z'', s60)) + TIMESITER(s61, z'', s62) + s1 :|: s57 >= 0, s57 <= z', s58 >= 0, s58 <= z4, s59 >= 0, s59 <= z', s60 >= 0, s60 <= 1 + z4, s61 >= 0, s61 <= z', s62 >= 0, s62 <= 1 + z4, s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(s63, z'', s64), timesIter(s65, z'', s66)) + TIMESITER(s67, z'', s68) + s2 :|: s63 >= 0, s63 <= z', s64 >= 0, s64 <= z4, s65 >= 0, s65 <= z', s66 >= 0, s66 <= 1 + z4, s67 >= 0, s67 <= z', s68 >= 0, s68 <= 1 + z4, s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ z }-> 1 + s29 :|: s29 >= 0, s29 <= 0, z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s77) + s14 :|: s77 >= 0, s77 <= z'' - 1 + z', s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + s39 :|: s39 >= 0, s39 <= 0, s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s82) + s40 :|: s82 >= 0, s82 <= z'' - 1 + z', s40 >= 0, s40 <= 0, s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s41 :|: s41 >= 0, s41 <= 0, s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', z'', 0) + s32 :|: s32 >= 0, s32 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s30 :|: s30 >= 0, s30 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s74) + s5 :|: s74 >= 0, s74 <= z'' - 1 + z', s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s79) + s31 :|: s79 >= 0, s79 <= z'' - 1 + z', s31 >= 0, s31 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', z'', 0) + s35 :|: s35 >= 0, s35 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + s33 :|: s33 >= 0, s33 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s75) + s8 :|: s75 >= 0, s75 <= z'' - 1 + z', s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s80) + s34 :|: s80 >= 0, s80 <= z'' - 1 + z', s34 >= 0, s34 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s38 :|: s38 >= 0, s38 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s36 :|: s36 >= 0, s36 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s76) + s11 :|: s76 >= 0, s76 <= z'' - 1 + z', s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s81) + s37 :|: s81 >= 0, s81 <= z'' - 1 + z', s37 >= 0, s37 <= 0, z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', z'', 0) + s44 :|: s44 >= 0, s44 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + s42 :|: s42 >= 0, s42 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s78) + s17 :|: s78 >= 0, s78 <= z'' - 1 + z', s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s83) + s43 :|: s83 >= 0, s83 <= z'' - 1 + z', s43 >= 0, s43 <= 0, z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + s69 :|: s69 >= 0, s69 <= z - 2, z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(s70, z'', s71), timesIter(s72, z'', s73)) :|: s70 >= 0, s70 <= z', s71 >= 0, s71 <= z4, s72 >= 0, s72 <= z', s73 >= 0, s73 <= 1 + z4, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + s84 :|: s84 >= 0, s84 <= z - 1 + z', z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s26, 1 + (1 + (1 + (z - 3))), z', 0, z') :|: s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(s27, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s88) :|: s88 >= 0, s88 <= z'' - 1 + z', s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s28, 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + s85) :|: s85 >= 0, s85 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + s86) :|: s86 >= 0, s86 <= z'' - 1 + z', z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s87) :|: s87 >= 0, s87 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + s89) :|: s89 >= 0, s89 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {p}, {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] PLUS: runtime: O(n^1) [z], size: O(1) [0] half: runtime: O(1) [0], size: O(n^1) [z] plus: runtime: O(1) [0], size: O(n^1) [z + z'] p: runtime: ?, size: O(n^1) [z] ---------------------------------------- (83) 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: 0 ---------------------------------------- (84) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s45, z'', s46), timesIter(s47, z'', s48)) + TIMESITER(s49, z'', s50) + s' :|: s45 >= 0, s45 <= z', s46 >= 0, s46 <= z4, s47 >= 0, s47 <= z', s48 >= 0, s48 <= 1 + z4, s49 >= 0, s49 <= z', s50 >= 0, s50 <= z4, s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(s51, z'', s52), timesIter(s53, z'', s54)) + TIMESITER(s55, z'', s56) + s'' :|: s51 >= 0, s51 <= z', s52 >= 0, s52 <= z4, s53 >= 0, s53 <= z', s54 >= 0, s54 <= 1 + z4, s55 >= 0, s55 <= z', s56 >= 0, s56 <= z4, s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s57, z'', s58), timesIter(s59, z'', s60)) + TIMESITER(s61, z'', s62) + s1 :|: s57 >= 0, s57 <= z', s58 >= 0, s58 <= z4, s59 >= 0, s59 <= z', s60 >= 0, s60 <= 1 + z4, s61 >= 0, s61 <= z', s62 >= 0, s62 <= 1 + z4, s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(s63, z'', s64), timesIter(s65, z'', s66)) + TIMESITER(s67, z'', s68) + s2 :|: s63 >= 0, s63 <= z', s64 >= 0, s64 <= z4, s65 >= 0, s65 <= z', s66 >= 0, s66 <= 1 + z4, s67 >= 0, s67 <= z', s68 >= 0, s68 <= 1 + z4, s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ z }-> 1 + s29 :|: s29 >= 0, s29 <= 0, z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s77) + s14 :|: s77 >= 0, s77 <= z'' - 1 + z', s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + s39 :|: s39 >= 0, s39 <= 0, s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s82) + s40 :|: s82 >= 0, s82 <= z'' - 1 + z', s40 >= 0, s40 <= 0, s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s41 :|: s41 >= 0, s41 <= 0, s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', z'', 0) + s32 :|: s32 >= 0, s32 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s30 :|: s30 >= 0, s30 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s74) + s5 :|: s74 >= 0, s74 <= z'' - 1 + z', s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s79) + s31 :|: s79 >= 0, s79 <= z'' - 1 + z', s31 >= 0, s31 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', z'', 0) + s35 :|: s35 >= 0, s35 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + s33 :|: s33 >= 0, s33 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s75) + s8 :|: s75 >= 0, s75 <= z'' - 1 + z', s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s80) + s34 :|: s80 >= 0, s80 <= z'' - 1 + z', s34 >= 0, s34 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s38 :|: s38 >= 0, s38 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s36 :|: s36 >= 0, s36 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s76) + s11 :|: s76 >= 0, s76 <= z'' - 1 + z', s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s81) + s37 :|: s81 >= 0, s81 <= z'' - 1 + z', s37 >= 0, s37 <= 0, z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', z'', 0) + s44 :|: s44 >= 0, s44 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + s42 :|: s42 >= 0, s42 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s78) + s17 :|: s78 >= 0, s78 <= z'' - 1 + z', s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s83) + s43 :|: s83 >= 0, s83 <= z'' - 1 + z', s43 >= 0, s43 <= 0, z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + s69 :|: s69 >= 0, s69 <= z - 2, z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(s70, z'', s71), timesIter(s72, z'', s73)) :|: s70 >= 0, s70 <= z', s71 >= 0, s71 <= z4, s72 >= 0, s72 <= z', s73 >= 0, s73 <= 1 + z4, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + s84 :|: s84 >= 0, s84 <= z - 1 + z', z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s26, 1 + (1 + (1 + (z - 3))), z', 0, z') :|: s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(s27, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s88) :|: s88 >= 0, s88 <= z'' - 1 + z', s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s28, 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + s85) :|: s85 >= 0, s85 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + s86) :|: s86 >= 0, s86 <= z'' - 1 + z', z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s87) :|: s87 >= 0, s87 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + s89) :|: s89 >= 0, s89 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] PLUS: runtime: O(n^1) [z], size: O(1) [0] half: runtime: O(1) [0], size: O(n^1) [z] plus: runtime: O(1) [0], size: O(n^1) [z + z'] p: runtime: O(1) [0], size: O(n^1) [z] ---------------------------------------- (85) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (86) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s45, z'', s46), timesIter(s47, z'', s48)) + TIMESITER(s49, z'', s50) + s' :|: s45 >= 0, s45 <= z', s46 >= 0, s46 <= z4, s47 >= 0, s47 <= z', s48 >= 0, s48 <= 1 + z4, s49 >= 0, s49 <= z', s50 >= 0, s50 <= z4, s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(s51, z'', s52), timesIter(s53, z'', s54)) + TIMESITER(s55, z'', s56) + s'' :|: s51 >= 0, s51 <= z', s52 >= 0, s52 <= z4, s53 >= 0, s53 <= z', s54 >= 0, s54 <= 1 + z4, s55 >= 0, s55 <= z', s56 >= 0, s56 <= z4, s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s57, z'', s58), timesIter(s59, z'', s60)) + TIMESITER(s61, z'', s62) + s1 :|: s57 >= 0, s57 <= z', s58 >= 0, s58 <= z4, s59 >= 0, s59 <= z', s60 >= 0, s60 <= 1 + z4, s61 >= 0, s61 <= z', s62 >= 0, s62 <= 1 + z4, s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(s63, z'', s64), timesIter(s65, z'', s66)) + TIMESITER(s67, z'', s68) + s2 :|: s63 >= 0, s63 <= z', s64 >= 0, s64 <= z4, s65 >= 0, s65 <= z', s66 >= 0, s66 <= 1 + z4, s67 >= 0, s67 <= z', s68 >= 0, s68 <= 1 + z4, s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ z }-> 1 + s29 :|: s29 >= 0, s29 <= 0, z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s77) + s14 :|: s77 >= 0, s77 <= z'' - 1 + z', s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + s39 :|: s39 >= 0, s39 <= 0, s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s82) + s40 :|: s82 >= 0, s82 <= z'' - 1 + z', s40 >= 0, s40 <= 0, s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s41 :|: s41 >= 0, s41 <= 0, s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', z'', 0) + s32 :|: s32 >= 0, s32 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s30 :|: s30 >= 0, s30 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s74) + s5 :|: s74 >= 0, s74 <= z'' - 1 + z', s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s79) + s31 :|: s79 >= 0, s79 <= z'' - 1 + z', s31 >= 0, s31 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', z'', 0) + s35 :|: s35 >= 0, s35 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + s33 :|: s33 >= 0, s33 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s75) + s8 :|: s75 >= 0, s75 <= z'' - 1 + z', s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s80) + s34 :|: s80 >= 0, s80 <= z'' - 1 + z', s34 >= 0, s34 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s38 :|: s38 >= 0, s38 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s36 :|: s36 >= 0, s36 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s76) + s11 :|: s76 >= 0, s76 <= z'' - 1 + z', s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s81) + s37 :|: s81 >= 0, s81 <= z'' - 1 + z', s37 >= 0, s37 <= 0, z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', z'', 0) + s44 :|: s44 >= 0, s44 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + s42 :|: s42 >= 0, s42 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s78) + s17 :|: s78 >= 0, s78 <= z'' - 1 + z', s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s83) + s43 :|: s83 >= 0, s83 <= z'' - 1 + z', s43 >= 0, s43 <= 0, z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + s69 :|: s69 >= 0, s69 <= z - 2, z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(s70, z'', s71), timesIter(s72, z'', s73)) :|: s70 >= 0, s70 <= z', s71 >= 0, s71 <= z4, s72 >= 0, s72 <= z', s73 >= 0, s73 <= 1 + z4, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + s84 :|: s84 >= 0, s84 <= z - 1 + z', z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s26, 1 + (1 + (1 + (z - 3))), z', 0, z') :|: s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(s27, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s88) :|: s88 >= 0, s88 <= z'' - 1 + z', s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s28, 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + s85) :|: s85 >= 0, s85 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + s86) :|: s86 >= 0, s86 <= z'' - 1 + z', z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s87) :|: s87 >= 0, s87 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + s89) :|: s89 >= 0, s89 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] PLUS: runtime: O(n^1) [z], size: O(1) [0] half: runtime: O(1) [0], size: O(n^1) [z] plus: runtime: O(1) [0], size: O(n^1) [z + z'] p: runtime: O(1) [0], size: O(n^1) [z] ---------------------------------------- (87) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: timesIter after applying outer abstraction to obtain an ITS, resulting in: INF with polynomial bound: ? Computed SIZE bound using CoFloCo for: if after applying outer abstraction to obtain an ITS, resulting in: INF with polynomial bound: ? ---------------------------------------- (88) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s45, z'', s46), timesIter(s47, z'', s48)) + TIMESITER(s49, z'', s50) + s' :|: s45 >= 0, s45 <= z', s46 >= 0, s46 <= z4, s47 >= 0, s47 <= z', s48 >= 0, s48 <= 1 + z4, s49 >= 0, s49 <= z', s50 >= 0, s50 <= z4, s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(s51, z'', s52), timesIter(s53, z'', s54)) + TIMESITER(s55, z'', s56) + s'' :|: s51 >= 0, s51 <= z', s52 >= 0, s52 <= z4, s53 >= 0, s53 <= z', s54 >= 0, s54 <= 1 + z4, s55 >= 0, s55 <= z', s56 >= 0, s56 <= z4, s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s57, z'', s58), timesIter(s59, z'', s60)) + TIMESITER(s61, z'', s62) + s1 :|: s57 >= 0, s57 <= z', s58 >= 0, s58 <= z4, s59 >= 0, s59 <= z', s60 >= 0, s60 <= 1 + z4, s61 >= 0, s61 <= z', s62 >= 0, s62 <= 1 + z4, s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(s63, z'', s64), timesIter(s65, z'', s66)) + TIMESITER(s67, z'', s68) + s2 :|: s63 >= 0, s63 <= z', s64 >= 0, s64 <= z4, s65 >= 0, s65 <= z', s66 >= 0, s66 <= 1 + z4, s67 >= 0, s67 <= z', s68 >= 0, s68 <= 1 + z4, s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ z }-> 1 + s29 :|: s29 >= 0, s29 <= 0, z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s77) + s14 :|: s77 >= 0, s77 <= z'' - 1 + z', s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + s39 :|: s39 >= 0, s39 <= 0, s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s82) + s40 :|: s82 >= 0, s82 <= z'' - 1 + z', s40 >= 0, s40 <= 0, s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s41 :|: s41 >= 0, s41 <= 0, s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', z'', 0) + s32 :|: s32 >= 0, s32 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s30 :|: s30 >= 0, s30 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s74) + s5 :|: s74 >= 0, s74 <= z'' - 1 + z', s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s79) + s31 :|: s79 >= 0, s79 <= z'' - 1 + z', s31 >= 0, s31 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', z'', 0) + s35 :|: s35 >= 0, s35 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + s33 :|: s33 >= 0, s33 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s75) + s8 :|: s75 >= 0, s75 <= z'' - 1 + z', s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s80) + s34 :|: s80 >= 0, s80 <= z'' - 1 + z', s34 >= 0, s34 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s38 :|: s38 >= 0, s38 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s36 :|: s36 >= 0, s36 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s76) + s11 :|: s76 >= 0, s76 <= z'' - 1 + z', s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s81) + s37 :|: s81 >= 0, s81 <= z'' - 1 + z', s37 >= 0, s37 <= 0, z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', z'', 0) + s44 :|: s44 >= 0, s44 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + s42 :|: s42 >= 0, s42 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s78) + s17 :|: s78 >= 0, s78 <= z'' - 1 + z', s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s83) + s43 :|: s83 >= 0, s83 <= z'' - 1 + z', s43 >= 0, s43 <= 0, z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + s69 :|: s69 >= 0, s69 <= z - 2, z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(s70, z'', s71), timesIter(s72, z'', s73)) :|: s70 >= 0, s70 <= z', s71 >= 0, s71 <= z4, s72 >= 0, s72 <= z', s73 >= 0, s73 <= 1 + z4, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + s84 :|: s84 >= 0, s84 <= z - 1 + z', z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s26, 1 + (1 + (1 + (z - 3))), z', 0, z') :|: s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(s27, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s88) :|: s88 >= 0, s88 <= z'' - 1 + z', s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s28, 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + s85) :|: s85 >= 0, s85 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + s86) :|: s86 >= 0, s86 <= z'' - 1 + z', z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s87) :|: s87 >= 0, s87 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + s89) :|: s89 >= 0, s89 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {timesIter,if}, {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] PLUS: runtime: O(n^1) [z], size: O(1) [0] half: runtime: O(1) [0], size: O(n^1) [z] plus: runtime: O(1) [0], size: O(n^1) [z + z'] p: runtime: O(1) [0], size: O(n^1) [z] timesIter: runtime: ?, size: INF if: runtime: ?, size: INF ---------------------------------------- (89) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: timesIter after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 Computed RUNTIME bound using CoFloCo for: if after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (90) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s45, z'', s46), timesIter(s47, z'', s48)) + TIMESITER(s49, z'', s50) + s' :|: s45 >= 0, s45 <= z', s46 >= 0, s46 <= z4, s47 >= 0, s47 <= z', s48 >= 0, s48 <= 1 + z4, s49 >= 0, s49 <= z', s50 >= 0, s50 <= z4, s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z4 }-> 1 + PLUS(timesIter(s51, z'', s52), timesIter(s53, z'', s54)) + TIMESITER(s55, z'', s56) + s'' :|: s51 >= 0, s51 <= z', s52 >= 0, s52 <= z4, s53 >= 0, s53 <= z', s54 >= 0, s54 <= 1 + z4, s55 >= 0, s55 <= z', s56 >= 0, s56 <= z4, s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + z' }-> 1 + PLUS(timesIter(s57, z'', s58), timesIter(s59, z'', s60)) + TIMESITER(s61, z'', s62) + s1 :|: s57 >= 0, s57 <= z', s58 >= 0, s58 <= z4, s59 >= 0, s59 <= z', s60 >= 0, s60 <= 1 + z4, s61 >= 0, s61 <= z', s62 >= 0, s62 <= 1 + z4, s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + z4 }-> 1 + PLUS(timesIter(s63, z'', s64), timesIter(s65, z'', s66)) + TIMESITER(s67, z'', s68) + s2 :|: s63 >= 0, s63 <= z', s64 >= 0, s64 <= z4, s65 >= 0, s65 <= z', s66 >= 0, s66 <= 1 + z4, s67 >= 0, s67 <= z', s68 >= 0, s68 <= 1 + z4, s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ z }-> 1 + s29 :|: s29 >= 0, s29 <= 0, z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s77) + s14 :|: s77 >= 0, s77 <= z'' - 1 + z', s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + s39 :|: s39 >= 0, s39 <= 0, s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s82) + s40 :|: s82 >= 0, s82 <= z'' - 1 + z', s40 >= 0, s40 <= 0, s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s41 :|: s41 >= 0, s41 <= 0, s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', z'', 0) + s32 :|: s32 >= 0, s32 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s30 :|: s30 >= 0, s30 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s74) + s5 :|: s74 >= 0, s74 <= z'' - 1 + z', s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s79) + s31 :|: s79 >= 0, s79 <= z'' - 1 + z', s31 >= 0, s31 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', z'', 0) + s35 :|: s35 >= 0, s35 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + s33 :|: s33 >= 0, s33 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s75) + s8 :|: s75 >= 0, s75 <= z'' - 1 + z', s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s80) + s34 :|: s80 >= 0, s80 <= z'' - 1 + z', s34 >= 0, s34 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s38 :|: s38 >= 0, s38 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s36 :|: s36 >= 0, s36 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s76) + s11 :|: s76 >= 0, s76 <= z'' - 1 + z', s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s81) + s37 :|: s81 >= 0, s81 <= z'' - 1 + z', s37 >= 0, s37 <= 0, z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', z'', 0) + s44 :|: s44 >= 0, s44 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + s42 :|: s42 >= 0, s42 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s78) + s17 :|: s78 >= 0, s78 <= z'' - 1 + z', s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s83) + s43 :|: s83 >= 0, s83 <= z'' - 1 + z', s43 >= 0, s43 <= 0, z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + s69 :|: s69 >= 0, s69 <= z - 2, z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(z' - 1, z'', z5) :|: z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(s70, z'', s71), timesIter(s72, z'', s73)) :|: s70 >= 0, s70 <= z', s71 >= 0, s71 <= z4, s72 >= 0, s72 <= z', s73 >= 0, s73 <= 1 + z4, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + s84 :|: s84 >= 0, s84 <= z - 1 + z', z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s26, 1 + (1 + (1 + (z - 3))), z', 0, z') :|: s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> if(s27, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s88) :|: s88 >= 0, s88 <= z'' - 1 + z', s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(s28, 1 + (1 + (1 + (z - 3))), z', z'', 0) :|: s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', z'', 0) :|: z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(3, 0, z', 1 + (z'' - 1), 1 + s85) :|: s85 >= 0, s85 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', z'', 0) :|: z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> if(2, 1 + 0, z', 1 + (z'' - 1), 1 + s86) :|: s86 >= 0, s86 <= z'' - 1 + z', z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', z'', 0) :|: z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 0, z') :|: z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s87) :|: s87 >= 0, s87 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> if(0, z, z', z'', 0) :|: z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 0, z') :|: z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> if(0, z, z', 1 + (z'' - 1), 1 + s89) :|: s89 >= 0, s89 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] PLUS: runtime: O(n^1) [z], size: O(1) [0] half: runtime: O(1) [0], size: O(n^1) [z] plus: runtime: O(1) [0], size: O(n^1) [z + z'] p: runtime: O(1) [0], size: O(n^1) [z] timesIter: runtime: O(1) [0], size: INF if: runtime: O(1) [0], size: INF ---------------------------------------- (91) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (92) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + s99 + z4 }-> 1 + s101 + TIMESITER(s67, z'', s68) + s2 :|: s99 >= 0, s99 <= inf4, s100 >= 0, s100 <= inf5, s101 >= 0, s101 <= 0, s63 >= 0, s63 <= z', s64 >= 0, s64 <= z4, s65 >= 0, s65 <= z', s66 >= 0, s66 <= 1 + z4, s67 >= 0, s67 <= z', s68 >= 0, s68 <= 1 + z4, s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + s90 + z' }-> 1 + s92 + TIMESITER(s49, z'', s50) + s' :|: s90 >= 0, s90 <= inf, s91 >= 0, s91 <= inf', s92 >= 0, s92 <= 0, s45 >= 0, s45 <= z', s46 >= 0, s46 <= z4, s47 >= 0, s47 <= z', s48 >= 0, s48 <= 1 + z4, s49 >= 0, s49 <= z', s50 >= 0, s50 <= z4, s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + s93 + z4 }-> 1 + s95 + TIMESITER(s55, z'', s56) + s'' :|: s93 >= 0, s93 <= inf'', s94 >= 0, s94 <= inf1, s95 >= 0, s95 <= 0, s51 >= 0, s51 <= z', s52 >= 0, s52 <= z4, s53 >= 0, s53 <= z', s54 >= 0, s54 <= 1 + z4, s55 >= 0, s55 <= z', s56 >= 0, s56 <= z4, s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + s96 + z' }-> 1 + s98 + TIMESITER(s61, z'', s62) + s1 :|: s96 >= 0, s96 <= inf2, s97 >= 0, s97 <= inf3, s98 >= 0, s98 <= 0, s57 >= 0, s57 <= z', s58 >= 0, s58 <= z4, s59 >= 0, s59 <= z', s60 >= 0, s60 <= 1 + z4, s61 >= 0, s61 <= z', s62 >= 0, s62 <= 1 + z4, s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ z }-> 1 + s29 :|: s29 >= 0, s29 <= 0, z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s77) + s14 :|: s77 >= 0, s77 <= z'' - 1 + z', s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + s39 :|: s39 >= 0, s39 <= 0, s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s82) + s40 :|: s82 >= 0, s82 <= z'' - 1 + z', s40 >= 0, s40 <= 0, s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s41 :|: s41 >= 0, s41 <= 0, s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', z'', 0) + s32 :|: s32 >= 0, s32 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s30 :|: s30 >= 0, s30 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s74) + s5 :|: s74 >= 0, s74 <= z'' - 1 + z', s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s79) + s31 :|: s79 >= 0, s79 <= z'' - 1 + z', s31 >= 0, s31 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', z'', 0) + s35 :|: s35 >= 0, s35 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + s33 :|: s33 >= 0, s33 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s75) + s8 :|: s75 >= 0, s75 <= z'' - 1 + z', s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s80) + s34 :|: s80 >= 0, s80 <= z'' - 1 + z', s34 >= 0, s34 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s38 :|: s38 >= 0, s38 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s36 :|: s36 >= 0, s36 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s76) + s11 :|: s76 >= 0, s76 <= z'' - 1 + z', s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s81) + s37 :|: s81 >= 0, s81 <= z'' - 1 + z', s37 >= 0, s37 <= 0, z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', z'', 0) + s44 :|: s44 >= 0, s44 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + s42 :|: s42 >= 0, s42 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s78) + s17 :|: s78 >= 0, s78 <= z'' - 1 + z', s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s83) + s43 :|: s83 >= 0, s83 <= z'' - 1 + z', s43 >= 0, s43 <= 0, z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + s69 :|: s69 >= 0, s69 <= z - 2, z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> s117 :|: s117 >= 0, s117 <= inf21, z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> s118 :|: s118 >= 0, s118 <= inf22, z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> s119 :|: s119 >= 0, s119 <= inf23, z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> s122 :|: s120 >= 0, s120 <= inf24, s121 >= 0, s121 <= inf25, s122 >= 0, s122 <= s120 + s121, s70 >= 0, s70 <= z', s71 >= 0, s71 <= z4, s72 >= 0, s72 <= z', s73 >= 0, s73 <= 1 + z4, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + s84 :|: s84 >= 0, s84 <= z - 1 + z', z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> s102 :|: s102 >= 0, s102 <= inf6, z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> s103 :|: s103 >= 0, s103 <= inf7, s85 >= 0, s85 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> s104 :|: s104 >= 0, s104 <= inf8, z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> s105 :|: s105 >= 0, s105 <= inf9, z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> s106 :|: s106 >= 0, s106 <= inf10, s86 >= 0, s86 <= z'' - 1 + z', z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> s107 :|: s107 >= 0, s107 <= inf11, z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> s108 :|: s108 >= 0, s108 <= inf12, z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> s109 :|: s109 >= 0, s109 <= inf13, s87 >= 0, s87 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> s110 :|: s110 >= 0, s110 <= inf14, z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> s111 :|: s111 >= 0, s111 <= inf15, s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> s112 :|: s112 >= 0, s112 <= inf16, s88 >= 0, s88 <= z'' - 1 + z', s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> s113 :|: s113 >= 0, s113 <= inf17, s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> s114 :|: s114 >= 0, s114 <= inf18, z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> s115 :|: s115 >= 0, s115 <= inf19, s89 >= 0, s89 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> s116 :|: s116 >= 0, s116 <= inf20, z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] PLUS: runtime: O(n^1) [z], size: O(1) [0] half: runtime: O(1) [0], size: O(n^1) [z] plus: runtime: O(1) [0], size: O(n^1) [z + z'] p: runtime: O(1) [0], size: O(n^1) [z] timesIter: runtime: O(1) [0], size: INF if: runtime: O(1) [0], size: INF ---------------------------------------- (93) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: TIMESITER after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 Computed SIZE bound using CoFloCo for: IF after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (94) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + s99 + z4 }-> 1 + s101 + TIMESITER(s67, z'', s68) + s2 :|: s99 >= 0, s99 <= inf4, s100 >= 0, s100 <= inf5, s101 >= 0, s101 <= 0, s63 >= 0, s63 <= z', s64 >= 0, s64 <= z4, s65 >= 0, s65 <= z', s66 >= 0, s66 <= 1 + z4, s67 >= 0, s67 <= z', s68 >= 0, s68 <= 1 + z4, s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + s90 + z' }-> 1 + s92 + TIMESITER(s49, z'', s50) + s' :|: s90 >= 0, s90 <= inf, s91 >= 0, s91 <= inf', s92 >= 0, s92 <= 0, s45 >= 0, s45 <= z', s46 >= 0, s46 <= z4, s47 >= 0, s47 <= z', s48 >= 0, s48 <= 1 + z4, s49 >= 0, s49 <= z', s50 >= 0, s50 <= z4, s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + s93 + z4 }-> 1 + s95 + TIMESITER(s55, z'', s56) + s'' :|: s93 >= 0, s93 <= inf'', s94 >= 0, s94 <= inf1, s95 >= 0, s95 <= 0, s51 >= 0, s51 <= z', s52 >= 0, s52 <= z4, s53 >= 0, s53 <= z', s54 >= 0, s54 <= 1 + z4, s55 >= 0, s55 <= z', s56 >= 0, s56 <= z4, s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + s96 + z' }-> 1 + s98 + TIMESITER(s61, z'', s62) + s1 :|: s96 >= 0, s96 <= inf2, s97 >= 0, s97 <= inf3, s98 >= 0, s98 <= 0, s57 >= 0, s57 <= z', s58 >= 0, s58 <= z4, s59 >= 0, s59 <= z', s60 >= 0, s60 <= 1 + z4, s61 >= 0, s61 <= z', s62 >= 0, s62 <= 1 + z4, s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ z }-> 1 + s29 :|: s29 >= 0, s29 <= 0, z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s77) + s14 :|: s77 >= 0, s77 <= z'' - 1 + z', s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + s39 :|: s39 >= 0, s39 <= 0, s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s82) + s40 :|: s82 >= 0, s82 <= z'' - 1 + z', s40 >= 0, s40 <= 0, s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s41 :|: s41 >= 0, s41 <= 0, s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', z'', 0) + s32 :|: s32 >= 0, s32 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s30 :|: s30 >= 0, s30 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s74) + s5 :|: s74 >= 0, s74 <= z'' - 1 + z', s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s79) + s31 :|: s79 >= 0, s79 <= z'' - 1 + z', s31 >= 0, s31 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', z'', 0) + s35 :|: s35 >= 0, s35 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + s33 :|: s33 >= 0, s33 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s75) + s8 :|: s75 >= 0, s75 <= z'' - 1 + z', s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s80) + s34 :|: s80 >= 0, s80 <= z'' - 1 + z', s34 >= 0, s34 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s38 :|: s38 >= 0, s38 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s36 :|: s36 >= 0, s36 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s76) + s11 :|: s76 >= 0, s76 <= z'' - 1 + z', s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s81) + s37 :|: s81 >= 0, s81 <= z'' - 1 + z', s37 >= 0, s37 <= 0, z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', z'', 0) + s44 :|: s44 >= 0, s44 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + s42 :|: s42 >= 0, s42 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s78) + s17 :|: s78 >= 0, s78 <= z'' - 1 + z', s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s83) + s43 :|: s83 >= 0, s83 <= z'' - 1 + z', s43 >= 0, s43 <= 0, z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + s69 :|: s69 >= 0, s69 <= z - 2, z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> s117 :|: s117 >= 0, s117 <= inf21, z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> s118 :|: s118 >= 0, s118 <= inf22, z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> s119 :|: s119 >= 0, s119 <= inf23, z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> s122 :|: s120 >= 0, s120 <= inf24, s121 >= 0, s121 <= inf25, s122 >= 0, s122 <= s120 + s121, s70 >= 0, s70 <= z', s71 >= 0, s71 <= z4, s72 >= 0, s72 <= z', s73 >= 0, s73 <= 1 + z4, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + s84 :|: s84 >= 0, s84 <= z - 1 + z', z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> s102 :|: s102 >= 0, s102 <= inf6, z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> s103 :|: s103 >= 0, s103 <= inf7, s85 >= 0, s85 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> s104 :|: s104 >= 0, s104 <= inf8, z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> s105 :|: s105 >= 0, s105 <= inf9, z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> s106 :|: s106 >= 0, s106 <= inf10, s86 >= 0, s86 <= z'' - 1 + z', z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> s107 :|: s107 >= 0, s107 <= inf11, z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> s108 :|: s108 >= 0, s108 <= inf12, z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> s109 :|: s109 >= 0, s109 <= inf13, s87 >= 0, s87 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> s110 :|: s110 >= 0, s110 <= inf14, z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> s111 :|: s111 >= 0, s111 <= inf15, s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> s112 :|: s112 >= 0, s112 <= inf16, s88 >= 0, s88 <= z'' - 1 + z', s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> s113 :|: s113 >= 0, s113 <= inf17, s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> s114 :|: s114 >= 0, s114 <= inf18, z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> s115 :|: s115 >= 0, s115 <= inf19, s89 >= 0, s89 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> s116 :|: s116 >= 0, s116 <= inf20, z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] PLUS: runtime: O(n^1) [z], size: O(1) [0] half: runtime: O(1) [0], size: O(n^1) [z] plus: runtime: O(1) [0], size: O(n^1) [z + z'] p: runtime: O(1) [0], size: O(n^1) [z] timesIter: runtime: O(1) [0], size: INF if: runtime: O(1) [0], size: INF TIMESITER: runtime: ?, size: O(1) [0] IF: runtime: ?, size: O(1) [1] ---------------------------------------- (95) 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: ? ---------------------------------------- (96) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ -1 + z }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z - 3 >= 0 HALF(z) -{ -1 + z }-> 1 + s :|: s >= 0, s <= 0, z - 2 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(0, z'', z5) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(z' - 1, z'', z5) :|: z = 2, z'' >= 0, z' - 1 >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 2 + s99 + z4 }-> 1 + s101 + TIMESITER(s67, z'', s68) + s2 :|: s99 >= 0, s99 <= inf4, s100 >= 0, s100 <= inf5, s101 >= 0, s101 <= 0, s63 >= 0, s63 <= z', s64 >= 0, s64 <= z4, s65 >= 0, s65 <= z', s66 >= 0, s66 <= 1 + z4, s67 >= 0, s67 <= z', s68 >= 0, s68 <= 1 + z4, s2 >= 0, s2 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + s90 + z' }-> 1 + s92 + TIMESITER(s49, z'', s50) + s' :|: s90 >= 0, s90 <= inf, s91 >= 0, s91 <= inf', s92 >= 0, s92 <= 0, s45 >= 0, s45 <= z', s46 >= 0, s46 <= z4, s47 >= 0, s47 <= z', s48 >= 0, s48 <= 1 + z4, s49 >= 0, s49 <= z', s50 >= 0, s50 <= z4, s' >= 0, s' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + s93 + z4 }-> 1 + s95 + TIMESITER(s55, z'', s56) + s'' :|: s93 >= 0, s93 <= inf'', s94 >= 0, s94 <= inf1, s95 >= 0, s95 <= 0, s51 >= 0, s51 <= z', s52 >= 0, s52 <= z4, s53 >= 0, s53 <= z', s54 >= 0, s54 <= 1 + z4, s55 >= 0, s55 <= z', s56 >= 0, s56 <= z4, s'' >= 0, s'' <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 IF(z, z', z'', z4, z5) -{ 1 + s96 + z' }-> 1 + s98 + TIMESITER(s61, z'', s62) + s1 :|: s96 >= 0, s96 <= inf2, s97 >= 0, s97 <= inf3, s98 >= 0, s98 <= 0, s57 >= 0, s57 <= z', s58 >= 0, s58 <= z4, s59 >= 0, s59 <= z', s60 >= 0, s60 <= 1 + z4, s61 >= 0, s61 <= z', s62 >= 0, s62 <= 1 + z4, s1 >= 0, s1 <= 0, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 PLUS(z, z') -{ z }-> 1 + s29 :|: s29 >= 0, s29 <= 0, z' >= 0, z - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s19, 1 + (1 + (1 + (z - 3))), z', 0, z') + s13 :|: s19 >= 0, s19 <= 3, s13 >= 0, s13 <= 0, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s20, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s77) + s14 :|: s77 >= 0, s77 <= z'' - 1 + z', s20 >= 0, s20 <= 3, s14 >= 0, s14 <= 0, z' >= 0, z - 3 >= 0, z'' - 1 >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(s21, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s15 :|: s21 >= 0, s21 <= 3, s15 >= 0, s15 <= 0, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(s22, 1 + (1 + (1 + (z - 3))), z', 0, z') + s39 :|: s39 >= 0, s39 <= 0, s22 >= 0, s22 <= 3, z'' = 0, z' >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s23, 1 + (1 + (1 + (z - 3))), z', 1 + (z'' - 1), 1 + s82) + s40 :|: s82 >= 0, s82 <= z'' - 1 + z', s40 >= 0, s40 <= 0, s23 >= 0, s23 <= 3, z' >= 0, z'' - 1 >= 0, z - 3 >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(s24, 1 + (1 + (1 + (z - 3))), z', z'', 0) + s41 :|: s41 >= 0, s41 <= 0, s24 >= 0, s24 <= 3, z' >= 0, z - 3 >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', z'', 0) + s32 :|: s32 >= 0, s32 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', z'', 0) + s6 :|: s6 >= 0, s6 <= 0, z' >= 0, z = 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s30 :|: s30 >= 0, s30 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 0, z') + s4 :|: s4 >= 0, s4 <= 0, z'' = 0, z' >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s74) + s5 :|: s74 >= 0, s74 <= z'' - 1 + z', s5 >= 0, s5 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(3, 0, z', 1 + (z'' - 1), 1 + s79) + s31 :|: s79 >= 0, s79 <= z'' - 1 + z', s31 >= 0, s31 <= 0, z' >= 0, z'' - 1 >= 0, z = 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', z'', 0) + s35 :|: s35 >= 0, s35 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', z'', 0) + s9 :|: s9 >= 0, s9 <= 0, z' >= 0, z = 1 + 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(2, 1 + 0, z', 0, z') + s33 :|: s33 >= 0, s33 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 0, z') + s7 :|: s7 >= 0, s7 <= 0, z'' = 0, z' >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 2 }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s75) + s8 :|: s75 >= 0, s75 <= z'' - 1 + z', s8 >= 0, s8 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(2, 1 + 0, z', 1 + (z'' - 1), 1 + s80) + s34 :|: s80 >= 0, s80 <= z'' - 1 + z', s34 >= 0, s34 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s12 :|: s12 >= 0, s12 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', z'', 0) + s38 :|: s38 >= 0, s38 <= 0, z' >= 0, z = 1 + (1 + 0), z'' >= 0 TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s10 :|: s10 >= 0, s10 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(1, 1 + (1 + 0), z', 0, z') + s36 :|: s36 >= 0, s36 <= 0, z'' = 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 3 }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s76) + s11 :|: s76 >= 0, s76 <= z'' - 1 + z', s11 >= 0, s11 <= 0, z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(1, 1 + (1 + 0), z', 1 + (z'' - 1), 1 + s81) + s37 :|: s81 >= 0, s81 <= z'' - 1 + z', s37 >= 0, s37 <= 0, z'' - 1 >= 0, z' >= 0, z = 1 + (1 + 0) TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', z'', 0) + s18 :|: s18 >= 0, s18 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', z'', 0) + s44 :|: s44 >= 0, s44 <= 0, z' >= 0, z >= 0, z'' >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 0, z') + s16 :|: s16 >= 0, s16 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(0, z, z', 0, z') + s42 :|: s42 >= 0, s42 <= 0, z'' = 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s78) + s17 :|: s78 >= 0, s78 <= z'' - 1 + z', s17 >= 0, s17 <= 0, z'' - 1 >= 0, z' >= 0, z >= 0 TIMESITER(z, z', z'') -{ 1 + z'' }-> 1 + IF(0, z, z', 1 + (z'' - 1), 1 + s83) + s43 :|: s83 >= 0, s83 <= z'' - 1 + z', s43 >= 0, s43 <= 0, z' >= 0, z >= 0, z'' - 1 >= 0 check(z) -{ 0 }-> s25 :|: s25 >= 0, s25 <= 3, z - 3 >= 0 check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: z >= 0 half(z) -{ 0 }-> 1 + s69 :|: s69 >= 0, s69 <= z - 2, z - 2 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> s117 :|: s117 >= 0, s117 <= inf21, z = 2, z' - 1 >= 0, z'' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> s118 :|: s118 >= 0, s118 <= inf22, z = 2, z'' >= 0, z4 >= 0, z5 >= 0, z' = 0 if(z, z', z'', z4, z5) -{ 0 }-> s119 :|: s119 >= 0, s119 <= inf23, z = 2, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> s122 :|: s120 >= 0, s120 <= inf24, s121 >= 0, s121 <= inf25, s122 >= 0, s122 <= s120 + s121, s70 >= 0, s70 <= z', s71 >= 0, s71 <= z4, s72 >= 0, s72 <= z', s73 >= 0, s73 <= 1 + z4, z'' >= 0, z = 1, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> z4 :|: z = 3, z'' >= 0, z' >= 0, z4 >= 0, z5 >= 0 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z >= 0, z5 >= 0, z' >= 0, z'' >= 0, z4 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: z >= 0 p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0 plus(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + s84 :|: s84 >= 0, s84 <= z - 1 + z', z' >= 0, z - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> s102 :|: s102 >= 0, s102 <= inf6, z'' = 0, z' >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> s103 :|: s103 >= 0, s103 <= inf7, s85 >= 0, s85 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 0 timesIter(z, z', z'') -{ 0 }-> s104 :|: s104 >= 0, s104 <= inf8, z' >= 0, z = 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> s105 :|: s105 >= 0, s105 <= inf9, z'' = 0, z' >= 0, z = 1 + 0 timesIter(z, z', z'') -{ 0 }-> s106 :|: s106 >= 0, s106 <= inf10, s86 >= 0, s86 <= z'' - 1 + z', z' >= 0, z = 1 + 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> s107 :|: s107 >= 0, s107 <= inf11, z' >= 0, z = 1 + 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> s108 :|: s108 >= 0, s108 <= inf12, z'' = 0, z' >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> s109 :|: s109 >= 0, s109 <= inf13, s87 >= 0, s87 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z = 1 + (1 + 0) timesIter(z, z', z'') -{ 0 }-> s110 :|: s110 >= 0, s110 <= inf14, z' >= 0, z = 1 + (1 + 0), z'' >= 0 timesIter(z, z', z'') -{ 0 }-> s111 :|: s111 >= 0, s111 <= inf15, s26 >= 0, s26 <= 3, z'' = 0, z - 3 >= 0, z' >= 0 timesIter(z, z', z'') -{ 0 }-> s112 :|: s112 >= 0, s112 <= inf16, s88 >= 0, s88 <= z'' - 1 + z', s27 >= 0, s27 <= 3, z - 3 >= 0, z' >= 0, z'' - 1 >= 0 timesIter(z, z', z'') -{ 0 }-> s113 :|: s113 >= 0, s113 <= inf17, s28 >= 0, s28 <= 3, z - 3 >= 0, z' >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> s114 :|: s114 >= 0, s114 <= inf18, z'' = 0, z' >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> s115 :|: s115 >= 0, s115 <= inf19, s89 >= 0, s89 <= z'' - 1 + z', z' >= 0, z'' - 1 >= 0, z >= 0 timesIter(z, z', z'') -{ 0 }-> s116 :|: s116 >= 0, s116 <= inf20, z' >= 0, z >= 0, z'' >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 Function symbols to be analyzed: {TIMESITER,IF} Previous analysis results are: HALF: runtime: O(n^1) [z], size: O(1) [0] CHECK: runtime: O(n^1) [z], size: O(1) [0] check: runtime: O(1) [0], size: O(1) [3] PLUS: runtime: O(n^1) [z], size: O(1) [0] half: runtime: O(1) [0], size: O(n^1) [z] plus: runtime: O(1) [0], size: O(n^1) [z + z'] p: runtime: O(1) [0], size: O(n^1) [z] timesIter: runtime: O(1) [0], size: INF if: runtime: O(1) [0], size: INF TIMESITER: runtime: INF, size: O(1) [0] IF: runtime: ?, size: O(1) [1] ---------------------------------------- (97) 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: check(v0) -> null_check [0] plus(v0, v1) -> null_plus [0] timesIter(v0, v1, v2) -> null_timesIter [0] half(v0) -> null_half [0] if(v0, v1, v2, v3, v4) -> null_if [0] p(v0) -> null_p [0] CHECK(v0) -> null_CHECK [0] HALF(v0) -> null_HALF [0] PLUS(v0, v1) -> null_PLUS [0] IF(v0, v1, v2, v3, v4) -> null_IF [0] And the following fresh constants: null_check, null_plus, null_timesIter, null_half, null_if, null_p, null_CHECK, null_HALF, null_PLUS, null_IF, const ---------------------------------------- (98) 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(s(s(s(z0)))) -> c3(CHECK(s(z0))) [1] HALF(s(s(z0))) -> c6(HALF(z0)) [1] PLUS(s(z0), z1) -> c8(PLUS(z0, z1)) [1] TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0)) [1] TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) [1] 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)) [1] 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)) [1] 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)) [1] 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))) [1] IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3)) [1] check(0) -> zero [0] check(s(0)) -> odd [0] check(s(s(0))) -> even [0] check(s(s(s(z0)))) -> check(s(z0)) [0] plus(0, z0) -> z0 [0] plus(s(z0), z1) -> s(plus(z0, z1)) [0] timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1)) [0] half(0) -> 0 [0] half(s(0)) -> 0 [0] half(s(s(z0))) -> s(half(z0)) [0] if(zero, z0, z1, z2, z3) -> z2 [0] if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3) [0] if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))) [0] p(s(z0)) -> z0 [0] p(0) -> 0 [0] check(v0) -> null_check [0] plus(v0, v1) -> null_plus [0] timesIter(v0, v1, v2) -> null_timesIter [0] half(v0) -> null_half [0] if(v0, v1, v2, v3, v4) -> null_if [0] p(v0) -> null_p [0] CHECK(v0) -> null_CHECK [0] HALF(v0) -> null_HALF [0] PLUS(v0, v1) -> null_PLUS [0] IF(v0, v1, v2, v3, v4) -> null_IF [0] The TRS has the following type information: CHECK :: s:0:null_plus:null_timesIter:null_half:null_if:null_p -> c3:null_CHECK s :: s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p c3 :: c3:null_CHECK -> c3:null_CHECK HALF :: s:0:null_plus:null_timesIter:null_half:null_if:null_p -> c6:null_HALF c6 :: c6:null_HALF -> c6:null_HALF PLUS :: s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p -> c8:null_PLUS c8 :: c8:null_PLUS -> c8:null_PLUS TIMESITER :: s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p -> c10:c11 c10 :: c16:c17:c18:c19:c15:null_IF -> c3:null_CHECK -> c10:c11 IF :: even:odd:zero:null_check -> s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p -> c16:c17:c18:c19:c15:null_IF check :: s:0:null_plus:null_timesIter:null_half:null_if:null_p -> even:odd:zero:null_check plus :: s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p c11 :: c16:c17:c18:c19:c15:null_IF -> c8:null_PLUS -> c10:c11 even :: even:odd:zero:null_check c16 :: c8:null_PLUS -> c10:c11 -> c6:null_HALF -> c16:c17:c18:c19:c15:null_IF timesIter :: s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p half :: s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p c17 :: c8:null_PLUS -> c10:c11 -> c6:null_HALF -> c16:c17:c18:c19:c15:null_IF c18 :: c8:null_PLUS -> c10:c11 -> c6:null_HALF -> c16:c17:c18:c19:c15:null_IF c19 :: c8:null_PLUS -> c10:c11 -> c6:null_HALF -> c16:c17:c18:c19:c15:null_IF odd :: even:odd:zero:null_check c15 :: c10:c11 -> c16:c17:c18:c19:c15:null_IF p :: s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p 0 :: s:0:null_plus:null_timesIter:null_half:null_if:null_p zero :: even:odd:zero:null_check if :: even:odd:zero:null_check -> s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p -> s:0:null_plus:null_timesIter:null_half:null_if:null_p null_check :: even:odd:zero:null_check null_plus :: s:0:null_plus:null_timesIter:null_half:null_if:null_p null_timesIter :: s:0:null_plus:null_timesIter:null_half:null_if:null_p null_half :: s:0:null_plus:null_timesIter:null_half:null_if:null_p null_if :: s:0:null_plus:null_timesIter:null_half:null_if:null_p null_p :: s:0:null_plus:null_timesIter:null_half:null_if:null_p null_CHECK :: c3:null_CHECK null_HALF :: c6:null_HALF null_PLUS :: c8:null_PLUS null_IF :: c16:c17:c18:c19:c15:null_IF const :: c10:c11 Rewrite Strategy: INNERMOST ---------------------------------------- (99) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: even => 1 odd => 2 0 => 0 zero => 3 null_check => 0 null_plus => 0 null_timesIter => 0 null_half => 0 null_if => 0 null_p => 0 null_CHECK => 0 null_HALF => 0 null_PLUS => 0 null_IF => 0 const => 0 ---------------------------------------- (100) Obligation: Complexity RNTS consisting of the following rules: CHECK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 CHECK(z) -{ 1 }-> 1 + CHECK(1 + z0) :|: z0 >= 0, z = 1 + (1 + (1 + z0)) HALF(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 HALF(z) -{ 1 }-> 1 + HALF(z0) :|: z0 >= 0, z = 1 + (1 + z0) IF(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z5 = v4, v0 >= 0, v4 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + TIMESITER(p(z0), z1, z3) :|: z = 2, z1 >= 0, z0 >= 0, z5 = z3, z' = z0, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(1 + z2))) + TIMESITER(half(z0), z1, half(z2)) + HALF(z0) :|: z1 >= 0, z = 1, z0 >= 0, z5 = z3, z' = z0, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(1 + z2))) + TIMESITER(half(z0), z1, half(z2)) + HALF(z2) :|: z1 >= 0, z = 1, z0 >= 0, z5 = z3, z' = z0, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(1 + z2))) + TIMESITER(half(z0), z1, half(1 + z2)) + HALF(z0) :|: z1 >= 0, z = 1, z0 >= 0, z5 = z3, z' = z0, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 IF(z, z', z'', z4, z5) -{ 1 }-> 1 + PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(1 + z2))) + TIMESITER(half(z0), z1, half(1 + z2)) + HALF(1 + z2) :|: z1 >= 0, z = 1, z0 >= 0, z5 = z3, z' = z0, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 PLUS(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 PLUS(z, z') -{ 1 }-> 1 + PLUS(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(z0), z0, z1, z2, plus(z2, z1)) + PLUS(z2, z1) :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 TIMESITER(z, z', z'') -{ 1 }-> 1 + IF(check(z0), z0, z1, z2, plus(z2, z1)) + CHECK(z0) :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 check(z) -{ 0 }-> check(1 + z0) :|: z0 >= 0, z = 1 + (1 + (1 + z0)) check(z) -{ 0 }-> 3 :|: z = 0 check(z) -{ 0 }-> 2 :|: z = 1 + 0 check(z) -{ 0 }-> 1 :|: z = 1 + (1 + 0) check(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 half(z) -{ 0 }-> 0 :|: z = 0 half(z) -{ 0 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 half(z) -{ 0 }-> 1 + half(z0) :|: z0 >= 0, z = 1 + (1 + z0) if(z, z', z'', z4, z5) -{ 0 }-> z2 :|: z = 3, z1 >= 0, z0 >= 0, z5 = z3, z' = z0, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 if(z, z', z'', z4, z5) -{ 0 }-> timesIter(p(z0), z1, z3) :|: z = 2, z1 >= 0, z0 >= 0, z5 = z3, z' = z0, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 if(z, z', z'', z4, z5) -{ 0 }-> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(1 + z2))) :|: z1 >= 0, z = 1, z0 >= 0, z5 = z3, z' = z0, z2 >= 0, z3 >= 0, z'' = z1, z4 = z2 if(z, z', z'', z4, z5) -{ 0 }-> 0 :|: z5 = v4, v0 >= 0, v4 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 p(z) -{ 0 }-> z0 :|: z = 1 + z0, z0 >= 0 p(z) -{ 0 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 plus(z, z') -{ 0 }-> z0 :|: z0 >= 0, z = 0, z' = z0 plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 plus(z, z') -{ 0 }-> 1 + plus(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 timesIter(z, z', z'') -{ 0 }-> if(check(z0), z0, z1, z2, plus(z2, z1)) :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 timesIter(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (101) 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))))) ---------------------------------------- (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)) 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 ---------------------------------------- (103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: TIMESITER(0, x1, x2) -> c10(IF(zero, 0, x1, x2, plus(x2, x1)), CHECK(0)) ---------------------------------------- (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)) 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 ---------------------------------------- (105) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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)) 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 ---------------------------------------- (107) 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)) ---------------------------------------- (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(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 ---------------------------------------- (109) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (111) 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] ---------------------------------------- (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(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 ---------------------------------------- (113) 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)))) ---------------------------------------- (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(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 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (117) 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)) ---------------------------------------- (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(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 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (121) 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)))) ---------------------------------------- (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(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 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (125) 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))) ---------------------------------------- (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(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 ---------------------------------------- (127) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (129) 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))))) ---------------------------------------- (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(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 ---------------------------------------- (131) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: TIMESITER(0, x1, 0) -> c10(IF(zero, 0, x1, 0, x1), CHECK(0)) ---------------------------------------- (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(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 ---------------------------------------- (133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 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(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 ---------------------------------------- (135) 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))))) ---------------------------------------- (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(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 ---------------------------------------- (137) 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)) ---------------------------------------- (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(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 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 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(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 ---------------------------------------- (141) 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))))) ---------------------------------------- (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(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 ---------------------------------------- (143) 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] ---------------------------------------- (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(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 ---------------------------------------- (145) 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)) ---------------------------------------- (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(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 ---------------------------------------- (147) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (149) 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] ---------------------------------------- (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(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 ---------------------------------------- (151) 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)) ---------------------------------------- (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(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 ---------------------------------------- (153) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (155) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (157) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: TIMESITER(0, x1, 0) -> c11(IF(zero, 0, x1, 0, x1)) ---------------------------------------- (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, 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 ---------------------------------------- (159) 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)))) ---------------------------------------- (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, 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 ---------------------------------------- (161) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (163) 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)))) ---------------------------------------- (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, 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 ---------------------------------------- (165) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (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, 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 ---------------------------------------- (169) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (171) 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)))) ---------------------------------------- (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(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 ---------------------------------------- (173) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (175) 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)))) ---------------------------------------- (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, 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 ---------------------------------------- (177) 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)))) ---------------------------------------- (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, 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 ---------------------------------------- (179) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (181) 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)))) ---------------------------------------- (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, 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 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (185) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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(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 ---------------------------------------- (187) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (189) 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)))) ---------------------------------------- (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, 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 ---------------------------------------- (191) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (193) 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))))) ---------------------------------------- (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(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 ---------------------------------------- (195) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (197) 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)))))) ---------------------------------------- (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, 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 ---------------------------------------- (199) 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))) ---------------------------------------- (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(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 ---------------------------------------- (201) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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(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 ---------------------------------------- (203) 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)) ---------------------------------------- (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(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 ---------------------------------------- (205) 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))) ---------------------------------------- (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, 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 ---------------------------------------- (207) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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, 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 ---------------------------------------- (209) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (211) 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))))) ---------------------------------------- (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, 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 ---------------------------------------- (213) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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, 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 ---------------------------------------- (215) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (217) 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))))) ---------------------------------------- (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, 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 ---------------------------------------- (219) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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, 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 ---------------------------------------- (221) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (223) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (225) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (227) 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))) ---------------------------------------- (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, 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 ---------------------------------------- (229) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (231) 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)) ---------------------------------------- (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(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 ---------------------------------------- (233) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (235) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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, 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 ---------------------------------------- (237) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (239) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (241) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (243) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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, 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 ---------------------------------------- (245) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (247) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (249) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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) -> 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 ---------------------------------------- (251) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (253) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 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, 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 ---------------------------------------- (255) 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)))) ---------------------------------------- (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, 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 ---------------------------------------- (257) 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)))) ---------------------------------------- (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, 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 ---------------------------------------- (259) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (261) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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, 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 ---------------------------------------- (263) 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)) ---------------------------------------- (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(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 ---------------------------------------- (265) 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)))) ---------------------------------------- (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) -> 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 ---------------------------------------- (267) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (269) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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, 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 ---------------------------------------- (271) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (273) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (275) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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, 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 ---------------------------------------- (277) 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))) ---------------------------------------- (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, 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 ---------------------------------------- (279) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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, 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 ---------------------------------------- (281) 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)) ---------------------------------------- (282) 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 ---------------------------------------- (283) 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))) ---------------------------------------- (284) 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 ---------------------------------------- (285) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (286) 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 ---------------------------------------- (287) 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)) ---------------------------------------- (288) 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 ---------------------------------------- (289) 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)))) ---------------------------------------- (290) 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 ---------------------------------------- (291) 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)))) ---------------------------------------- (292) 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 ---------------------------------------- (293) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (294) 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 ---------------------------------------- (295) 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)))) ---------------------------------------- (296) 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 ---------------------------------------- (297) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (298) 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 ---------------------------------------- (299) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (300) 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 ---------------------------------------- (301) 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)) ---------------------------------------- (302) 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 ---------------------------------------- (303) 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))))) ---------------------------------------- (304) 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 ---------------------------------------- (305) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (306) 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 ---------------------------------------- (307) 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)))) ---------------------------------------- (308) 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 ---------------------------------------- (309) 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)))) ---------------------------------------- (310) 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 ---------------------------------------- (311) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (312) 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 ---------------------------------------- (313) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (314) 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 ---------------------------------------- (315) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (316) 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 ---------------------------------------- (317) 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 ---------------------------------------- (318) 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 ---------------------------------------- (319) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (320) 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 ---------------------------------------- (321) 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 ---------------------------------------- (322) 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 ---------------------------------------- (323) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (324) 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 ---------------------------------------- (325) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID)) Found the following analysis order by SCC decomposition: { check } { half } { plus } { p } { timesIter, if } { times } ---------------------------------------- (326) 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} ---------------------------------------- (327) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (328) 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} ---------------------------------------- (329) 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 ---------------------------------------- (330) 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] ---------------------------------------- (331) 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' ---------------------------------------- (332) 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] ---------------------------------------- (333) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (334) 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] ---------------------------------------- (335) 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' ---------------------------------------- (336) 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'] ---------------------------------------- (337) 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' ---------------------------------------- (338) 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'] ---------------------------------------- (339) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (340) 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'] ---------------------------------------- (341) 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'' ---------------------------------------- (342) 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''] ---------------------------------------- (343) 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' ---------------------------------------- (344) 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''] ---------------------------------------- (345) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (346) 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''] ---------------------------------------- (347) 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' ---------------------------------------- (348) 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'] ---------------------------------------- (349) 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 ---------------------------------------- (350) 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'] ---------------------------------------- (351) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (352) 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'] ---------------------------------------- (353) 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: ? ---------------------------------------- (354) 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 ---------------------------------------- (355) 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: ? ---------------------------------------- (356) 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 ---------------------------------------- (357) 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 ---------------------------------------- (358) 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 ---------------------------------------- (359) 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 ---------------------------------------- (360) 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.