/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could not be shown: (0) HASKELL (1) IFR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4) HASKELL (5) COR [EQUIVALENT, 0 ms] (6) HASKELL (7) LetRed [EQUIVALENT, 0 ms] (8) HASKELL (9) NumRed [SOUND, 0 ms] (10) HASKELL (11) Narrow [SOUND, 0 ms] (12) AND (13) QDP (14) MNOCProof [EQUIVALENT, 0 ms] (15) QDP (16) InductionCalculusProof [EQUIVALENT, 0 ms] (17) QDP (18) TransformationProof [EQUIVALENT, 0 ms] (19) QDP (20) DependencyGraphProof [EQUIVALENT, 0 ms] (21) AND (22) QDP (23) UsableRulesProof [EQUIVALENT, 0 ms] (24) QDP (25) QReductionProof [EQUIVALENT, 0 ms] (26) QDP (27) TransformationProof [EQUIVALENT, 2 ms] (28) QDP (29) DependencyGraphProof [EQUIVALENT, 0 ms] (30) AND (31) QDP (32) UsableRulesProof [EQUIVALENT, 0 ms] (33) QDP (34) QReductionProof [EQUIVALENT, 0 ms] (35) QDP (36) TransformationProof [EQUIVALENT, 0 ms] (37) QDP (38) TransformationProof [EQUIVALENT, 0 ms] (39) QDP (40) DependencyGraphProof [EQUIVALENT, 0 ms] (41) QDP (42) TransformationProof [EQUIVALENT, 0 ms] (43) QDP (44) TransformationProof [EQUIVALENT, 0 ms] (45) QDP (46) DependencyGraphProof [EQUIVALENT, 0 ms] (47) QDP (48) TransformationProof [EQUIVALENT, 0 ms] (49) QDP (50) TransformationProof [EQUIVALENT, 0 ms] (51) QDP (52) TransformationProof [EQUIVALENT, 0 ms] (53) QDP (54) DependencyGraphProof [EQUIVALENT, 0 ms] (55) QDP (56) TransformationProof [EQUIVALENT, 0 ms] (57) QDP (58) QDPSizeChangeProof [EQUIVALENT, 0 ms] (59) YES (60) QDP (61) UsableRulesProof [EQUIVALENT, 0 ms] (62) QDP (63) TransformationProof [EQUIVALENT, 0 ms] (64) QDP (65) DependencyGraphProof [EQUIVALENT, 0 ms] (66) AND (67) QDP (68) TransformationProof [EQUIVALENT, 0 ms] (69) QDP (70) TransformationProof [EQUIVALENT, 0 ms] (71) QDP (72) TransformationProof [EQUIVALENT, 0 ms] (73) QDP (74) TransformationProof [EQUIVALENT, 0 ms] (75) QDP (76) TransformationProof [EQUIVALENT, 0 ms] (77) QDP (78) DependencyGraphProof [EQUIVALENT, 0 ms] (79) QDP (80) TransformationProof [EQUIVALENT, 0 ms] (81) QDP (82) TransformationProof [EQUIVALENT, 0 ms] (83) QDP (84) DependencyGraphProof [EQUIVALENT, 0 ms] (85) QDP (86) QDPOrderProof [EQUIVALENT, 0 ms] (87) QDP (88) DependencyGraphProof [EQUIVALENT, 0 ms] (89) TRUE (90) QDP (91) TransformationProof [EQUIVALENT, 0 ms] (92) QDP (93) DependencyGraphProof [EQUIVALENT, 0 ms] (94) AND (95) QDP (96) TransformationProof [EQUIVALENT, 0 ms] (97) QDP (98) TransformationProof [EQUIVALENT, 0 ms] (99) QDP (100) TransformationProof [EQUIVALENT, 0 ms] (101) QDP (102) TransformationProof [EQUIVALENT, 1 ms] (103) QDP (104) TransformationProof [EQUIVALENT, 0 ms] (105) QDP (106) TransformationProof [EQUIVALENT, 0 ms] (107) QDP (108) TransformationProof [EQUIVALENT, 0 ms] (109) QDP (110) DependencyGraphProof [EQUIVALENT, 0 ms] (111) QDP (112) TransformationProof [EQUIVALENT, 0 ms] (113) QDP (114) QDPOrderProof [EQUIVALENT, 21 ms] (115) QDP (116) DependencyGraphProof [EQUIVALENT, 0 ms] (117) TRUE (118) QDP (119) InductionCalculusProof [EQUIVALENT, 0 ms] (120) QDP (121) QDP (122) UsableRulesProof [EQUIVALENT, 0 ms] (123) QDP (124) QReductionProof [EQUIVALENT, 0 ms] (125) QDP (126) TransformationProof [EQUIVALENT, 0 ms] (127) QDP (128) DependencyGraphProof [EQUIVALENT, 0 ms] (129) AND (130) QDP (131) UsableRulesProof [EQUIVALENT, 0 ms] (132) QDP (133) QReductionProof [EQUIVALENT, 0 ms] (134) QDP (135) TransformationProof [EQUIVALENT, 0 ms] (136) QDP (137) DependencyGraphProof [EQUIVALENT, 0 ms] (138) AND (139) QDP (140) UsableRulesProof [EQUIVALENT, 0 ms] (141) QDP (142) QReductionProof [EQUIVALENT, 0 ms] (143) QDP (144) TransformationProof [EQUIVALENT, 0 ms] (145) QDP (146) TransformationProof [EQUIVALENT, 0 ms] (147) QDP (148) DependencyGraphProof [EQUIVALENT, 0 ms] (149) QDP (150) TransformationProof [EQUIVALENT, 0 ms] (151) QDP (152) TransformationProof [EQUIVALENT, 0 ms] (153) QDP (154) TransformationProof [EQUIVALENT, 0 ms] (155) QDP (156) DependencyGraphProof [EQUIVALENT, 0 ms] (157) QDP (158) TransformationProof [EQUIVALENT, 0 ms] (159) QDP (160) TransformationProof [EQUIVALENT, 0 ms] (161) QDP (162) TransformationProof [EQUIVALENT, 0 ms] (163) QDP (164) DependencyGraphProof [EQUIVALENT, 0 ms] (165) QDP (166) QDPSizeChangeProof [EQUIVALENT, 0 ms] (167) YES (168) QDP (169) UsableRulesProof [EQUIVALENT, 0 ms] (170) QDP (171) TransformationProof [EQUIVALENT, 0 ms] (172) QDP (173) DependencyGraphProof [EQUIVALENT, 0 ms] (174) AND (175) QDP (176) TransformationProof [EQUIVALENT, 0 ms] (177) QDP (178) TransformationProof [EQUIVALENT, 0 ms] (179) QDP (180) TransformationProof [EQUIVALENT, 0 ms] (181) QDP (182) TransformationProof [EQUIVALENT, 0 ms] (183) QDP (184) TransformationProof [EQUIVALENT, 0 ms] (185) QDP (186) DependencyGraphProof [EQUIVALENT, 0 ms] (187) QDP (188) TransformationProof [EQUIVALENT, 0 ms] (189) QDP (190) TransformationProof [EQUIVALENT, 0 ms] (191) QDP (192) DependencyGraphProof [EQUIVALENT, 0 ms] (193) QDP (194) QDPOrderProof [EQUIVALENT, 16 ms] (195) QDP (196) DependencyGraphProof [EQUIVALENT, 0 ms] (197) TRUE (198) QDP (199) TransformationProof [EQUIVALENT, 0 ms] (200) QDP (201) DependencyGraphProof [EQUIVALENT, 0 ms] (202) AND (203) QDP (204) TransformationProof [EQUIVALENT, 0 ms] (205) QDP (206) TransformationProof [EQUIVALENT, 0 ms] (207) QDP (208) TransformationProof [EQUIVALENT, 0 ms] (209) QDP (210) TransformationProof [EQUIVALENT, 0 ms] (211) QDP (212) TransformationProof [EQUIVALENT, 0 ms] (213) QDP (214) TransformationProof [EQUIVALENT, 0 ms] (215) QDP (216) TransformationProof [EQUIVALENT, 0 ms] (217) QDP (218) DependencyGraphProof [EQUIVALENT, 0 ms] (219) QDP (220) TransformationProof [EQUIVALENT, 0 ms] (221) QDP (222) QDPOrderProof [EQUIVALENT, 0 ms] (223) QDP (224) DependencyGraphProof [EQUIVALENT, 0 ms] (225) TRUE (226) QDP (227) InductionCalculusProof [EQUIVALENT, 0 ms] (228) QDP (229) QDP (230) UsableRulesProof [EQUIVALENT, 0 ms] (231) QDP (232) QReductionProof [EQUIVALENT, 0 ms] (233) QDP (234) TransformationProof [EQUIVALENT, 0 ms] (235) QDP (236) DependencyGraphProof [EQUIVALENT, 0 ms] (237) QDP (238) TransformationProof [EQUIVALENT, 0 ms] (239) QDP (240) DependencyGraphProof [EQUIVALENT, 0 ms] (241) QDP (242) TransformationProof [EQUIVALENT, 0 ms] (243) QDP (244) TransformationProof [EQUIVALENT, 0 ms] (245) QDP (246) DependencyGraphProof [EQUIVALENT, 0 ms] (247) AND (248) QDP (249) UsableRulesProof [EQUIVALENT, 0 ms] (250) QDP (251) QReductionProof [EQUIVALENT, 0 ms] (252) QDP (253) TransformationProof [EQUIVALENT, 0 ms] (254) QDP (255) TransformationProof [EQUIVALENT, 0 ms] (256) QDP (257) TransformationProof [EQUIVALENT, 0 ms] (258) QDP (259) TransformationProof [EQUIVALENT, 0 ms] (260) QDP (261) DependencyGraphProof [EQUIVALENT, 0 ms] (262) QDP (263) TransformationProof [EQUIVALENT, 0 ms] (264) QDP (265) TransformationProof [EQUIVALENT, 0 ms] (266) QDP (267) TransformationProof [EQUIVALENT, 0 ms] (268) QDP (269) DependencyGraphProof [EQUIVALENT, 0 ms] (270) QDP (271) QDPSizeChangeProof [EQUIVALENT, 3 ms] (272) YES (273) QDP (274) UsableRulesProof [EQUIVALENT, 0 ms] (275) QDP (276) QReductionProof [EQUIVALENT, 0 ms] (277) QDP (278) TransformationProof [EQUIVALENT, 0 ms] (279) QDP (280) TransformationProof [EQUIVALENT, 0 ms] (281) QDP (282) TransformationProof [EQUIVALENT, 0 ms] (283) QDP (284) DependencyGraphProof [EQUIVALENT, 0 ms] (285) QDP (286) TransformationProof [EQUIVALENT, 0 ms] (287) QDP (288) TransformationProof [EQUIVALENT, 0 ms] (289) QDP (290) TransformationProof [EQUIVALENT, 0 ms] (291) QDP (292) DependencyGraphProof [EQUIVALENT, 0 ms] (293) QDP (294) QDPSizeChangeProof [EQUIVALENT, 0 ms] (295) YES (296) QDP (297) UsableRulesProof [EQUIVALENT, 0 ms] (298) QDP (299) TransformationProof [EQUIVALENT, 0 ms] (300) QDP (301) TransformationProof [EQUIVALENT, 0 ms] (302) QDP (303) TransformationProof [EQUIVALENT, 0 ms] (304) QDP (305) TransformationProof [EQUIVALENT, 0 ms] (306) QDP (307) TransformationProof [EQUIVALENT, 0 ms] (308) QDP (309) TransformationProof [EQUIVALENT, 0 ms] (310) QDP (311) DependencyGraphProof [EQUIVALENT, 0 ms] (312) QDP (313) TransformationProof [EQUIVALENT, 0 ms] (314) QDP (315) TransformationProof [EQUIVALENT, 0 ms] (316) QDP (317) TransformationProof [EQUIVALENT, 0 ms] (318) QDP (319) TransformationProof [EQUIVALENT, 0 ms] (320) QDP (321) TransformationProof [EQUIVALENT, 0 ms] (322) QDP (323) TransformationProof [EQUIVALENT, 0 ms] (324) QDP (325) TransformationProof [EQUIVALENT, 0 ms] (326) QDP (327) TransformationProof [EQUIVALENT, 0 ms] (328) QDP (329) TransformationProof [EQUIVALENT, 0 ms] (330) QDP (331) DependencyGraphProof [EQUIVALENT, 0 ms] (332) QDP (333) TransformationProof [EQUIVALENT, 0 ms] (334) QDP (335) TransformationProof [EQUIVALENT, 0 ms] (336) QDP (337) DependencyGraphProof [EQUIVALENT, 0 ms] (338) AND (339) QDP (340) TransformationProof [EQUIVALENT, 0 ms] (341) QDP (342) TransformationProof [EQUIVALENT, 0 ms] (343) QDP (344) TransformationProof [EQUIVALENT, 0 ms] (345) QDP (346) TransformationProof [EQUIVALENT, 0 ms] (347) QDP (348) DependencyGraphProof [EQUIVALENT, 0 ms] (349) QDP (350) QDPOrderProof [EQUIVALENT, 94 ms] (351) QDP (352) DependencyGraphProof [EQUIVALENT, 0 ms] (353) TRUE (354) QDP (355) TransformationProof [EQUIVALENT, 0 ms] (356) QDP (357) DependencyGraphProof [EQUIVALENT, 0 ms] (358) QDP (359) QDPOrderProof [EQUIVALENT, 87 ms] (360) QDP (361) DependencyGraphProof [EQUIVALENT, 0 ms] (362) TRUE (363) QDP (364) TransformationProof [EQUIVALENT, 0 ms] (365) QDP (366) DependencyGraphProof [EQUIVALENT, 0 ms] (367) AND (368) QDP (369) TransformationProof [EQUIVALENT, 0 ms] (370) QDP (371) TransformationProof [EQUIVALENT, 0 ms] (372) QDP (373) TransformationProof [EQUIVALENT, 0 ms] (374) QDP (375) TransformationProof [EQUIVALENT, 0 ms] (376) QDP (377) QDPOrderProof [EQUIVALENT, 15 ms] (378) QDP (379) DependencyGraphProof [EQUIVALENT, 0 ms] (380) TRUE (381) QDP (382) QDPOrderProof [EQUIVALENT, 76 ms] (383) QDP (384) DependencyGraphProof [EQUIVALENT, 0 ms] (385) TRUE (386) QDP (387) InductionCalculusProof [EQUIVALENT, 0 ms] (388) QDP (389) QDP (390) QDPSizeChangeProof [EQUIVALENT, 0 ms] (391) YES (392) QDP (393) QDPSizeChangeProof [EQUIVALENT, 0 ms] (394) YES (395) QDP (396) QDPSizeChangeProof [EQUIVALENT, 0 ms] (397) YES (398) QDP (399) DependencyGraphProof [EQUIVALENT, 0 ms] (400) AND (401) QDP (402) TransformationProof [EQUIVALENT, 0 ms] (403) QDP (404) TransformationProof [EQUIVALENT, 0 ms] (405) QDP (406) QDPSizeChangeProof [EQUIVALENT, 0 ms] (407) YES (408) QDP (409) QDPSizeChangeProof [EQUIVALENT, 0 ms] (410) YES (411) QDP (412) DependencyGraphProof [EQUIVALENT, 0 ms] (413) AND (414) QDP (415) MRRProof [EQUIVALENT, 0 ms] (416) QDP (417) PisEmptyProof [EQUIVALENT, 0 ms] (418) YES (419) QDP (420) QDPSizeChangeProof [EQUIVALENT, 0 ms] (421) YES (422) QDP (423) QDPSizeChangeProof [EQUIVALENT, 0 ms] (424) YES (425) QDP (426) QDPSizeChangeProof [EQUIVALENT, 0 ms] (427) YES (428) QDP (429) QDPSizeChangeProof [EQUIVALENT, 0 ms] (430) YES (431) QDP (432) QDPSizeChangeProof [EQUIVALENT, 0 ms] (433) YES (434) Narrow [COMPLETE, 0 ms] (435) TRUE ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (1) IFR (EQUIVALENT) If Reductions: The following If expression "if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero" is transformed to "primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y)); primDivNatS0 x y False = Zero; " The following If expression "if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x" is transformed to "primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y); primModNatS0 x y False = Succ x; " ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (3) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (4) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (5) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "absReal x|x >= 0x|otherwise`negate` x; " is transformed to "absReal x = absReal2 x; " "absReal1 x True = x; absReal1 x False = absReal0 x otherwise; " "absReal0 x True = `negate` x; " "absReal2 x = absReal1 x (x >= 0); " The following Function with conditions "gcd' x 0 = x; gcd' x y = gcd' y (x `rem` y); " is transformed to "gcd' x xz = gcd'2 x xz; gcd' x y = gcd'0 x y; " "gcd'0 x y = gcd' y (x `rem` y); " "gcd'1 True x xz = x; gcd'1 yu yv yw = gcd'0 yv yw; " "gcd'2 x xz = gcd'1 (xz == 0) x xz; gcd'2 yx yy = gcd'0 yx yy; " The following Function with conditions "gcd 0 0 = error []; gcd x y = gcd' (abs x) (abs y) where { gcd' x 0 = x; gcd' x y = gcd' y (x `rem` y); } ; " is transformed to "gcd yz zu = gcd3 yz zu; gcd x y = gcd0 x y; " "gcd0 x y = gcd' (abs x) (abs y) where { gcd' x xz = gcd'2 x xz; gcd' x y = gcd'0 x y; ; gcd'0 x y = gcd' y (x `rem` y); ; gcd'1 True x xz = x; gcd'1 yu yv yw = gcd'0 yv yw; ; gcd'2 x xz = gcd'1 (xz == 0) x xz; gcd'2 yx yy = gcd'0 yx yy; } ; " "gcd1 True yz zu = error []; gcd1 zv zw zx = gcd0 zw zx; " "gcd2 True yz zu = gcd1 (zu == 0) yz zu; gcd2 zy zz vuu = gcd0 zz vuu; " "gcd3 yz zu = gcd2 (yz == 0) yz zu; gcd3 vuv vuw = gcd0 vuv vuw; " The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " The following Function with conditions "reduce x y|y == 0error []|otherwisex `quot` d :% (y `quot` d) where { d = gcd x y; } ; " is transformed to "reduce x y = reduce2 x y; " "reduce2 x y = reduce1 x y (y == 0) where { d = gcd x y; ; reduce0 x y True = x `quot` d :% (y `quot` d); ; reduce1 x y True = error []; reduce1 x y False = reduce0 x y otherwise; } ; " ---------------------------------------- (6) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (7) LetRed (EQUIVALENT) Let/Where Reductions: The bindings of the following Let/Where expression "gcd' (abs x) (abs y) where { gcd' x xz = gcd'2 x xz; gcd' x y = gcd'0 x y; ; gcd'0 x y = gcd' y (x `rem` y); ; gcd'1 True x xz = x; gcd'1 yu yv yw = gcd'0 yv yw; ; gcd'2 x xz = gcd'1 (xz == 0) x xz; gcd'2 yx yy = gcd'0 yx yy; } " are unpacked to the following functions on top level "gcd0Gcd' x xz = gcd0Gcd'2 x xz; gcd0Gcd' x y = gcd0Gcd'0 x y; " "gcd0Gcd'1 True x xz = x; gcd0Gcd'1 yu yv yw = gcd0Gcd'0 yv yw; " "gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y); " "gcd0Gcd'2 x xz = gcd0Gcd'1 (xz == 0) x xz; gcd0Gcd'2 yx yy = gcd0Gcd'0 yx yy; " The bindings of the following Let/Where expression "reduce1 x y (y == 0) where { d = gcd x y; ; reduce0 x y True = x `quot` d :% (y `quot` d); ; reduce1 x y True = error []; reduce1 x y False = reduce0 x y otherwise; } " are unpacked to the following functions on top level "reduce2D vux vuy = gcd vux vuy; " "reduce2Reduce0 vux vuy x y True = x `quot` reduce2D vux vuy :% (y `quot` reduce2D vux vuy); " "reduce2Reduce1 vux vuy x y True = error []; reduce2Reduce1 vux vuy x y False = reduce2Reduce0 vux vuy x y otherwise; " ---------------------------------------- (8) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (9) NumRed (SOUND) Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. ---------------------------------------- (10) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (11) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="(-)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="(-) vuz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="(-) vuz3 vuz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="vuz3 + (negate vuz4)",fontsize=16,color="burlywood",shape="box"];6382[label="vuz3/vuz30 :% vuz31",fontsize=10,color="white",style="solid",shape="box"];5 -> 6382[label="",style="solid", color="burlywood", weight=9]; 6382 -> 6[label="",style="solid", color="burlywood", weight=3]; 6[label="vuz30 :% vuz31 + (negate vuz4)",fontsize=16,color="burlywood",shape="box"];6383[label="vuz4/vuz40 :% vuz41",fontsize=10,color="white",style="solid",shape="box"];6 -> 6383[label="",style="solid", color="burlywood", weight=9]; 6383 -> 7[label="",style="solid", color="burlywood", weight=3]; 7[label="vuz30 :% vuz31 + (negate vuz40 :% vuz41)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 8[label="vuz30 :% vuz31 + (negate vuz40) :% vuz41",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 9[label="vuz30 :% vuz31 + primNegInt vuz40 :% vuz41",fontsize=16,color="burlywood",shape="box"];6384[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];9 -> 6384[label="",style="solid", color="burlywood", weight=9]; 6384 -> 10[label="",style="solid", color="burlywood", weight=3]; 6385[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];9 -> 6385[label="",style="solid", color="burlywood", weight=9]; 6385 -> 11[label="",style="solid", color="burlywood", weight=3]; 10[label="vuz30 :% vuz31 + primNegInt (Pos vuz400) :% vuz41",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3]; 11[label="vuz30 :% vuz31 + primNegInt (Neg vuz400) :% vuz41",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3]; 12[label="vuz30 :% vuz31 + Neg vuz400 :% vuz41",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3]; 13[label="vuz30 :% vuz31 + Pos vuz400 :% vuz41",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3]; 14[label="reduce (vuz30 * vuz41 + Neg vuz400 * vuz31) (vuz31 * vuz41)",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3]; 15[label="reduce (vuz30 * vuz41 + Pos vuz400 * vuz31) (vuz31 * vuz41)",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 16[label="reduce2 (vuz30 * vuz41 + Neg vuz400 * vuz31) (vuz31 * vuz41)",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3]; 17[label="reduce2 (vuz30 * vuz41 + Pos vuz400 * vuz31) (vuz31 * vuz41)",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3]; 18[label="reduce2Reduce1 (vuz30 * vuz41 + Neg vuz400 * vuz31) (vuz31 * vuz41) (vuz30 * vuz41 + Neg vuz400 * vuz31) (vuz31 * vuz41) (vuz31 * vuz41 == fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3]; 19[label="reduce2Reduce1 (vuz30 * vuz41 + Pos vuz400 * vuz31) (vuz31 * vuz41) (vuz30 * vuz41 + Pos vuz400 * vuz31) (vuz31 * vuz41) (vuz31 * vuz41 == fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3]; 20[label="reduce2Reduce1 (vuz30 * vuz41 + Neg vuz400 * vuz31) (vuz31 * vuz41) (vuz30 * vuz41 + Neg vuz400 * vuz31) (vuz31 * vuz41) (primEqInt (vuz31 * vuz41) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3]; 21[label="reduce2Reduce1 (vuz30 * vuz41 + Pos vuz400 * vuz31) (vuz31 * vuz41) (vuz30 * vuz41 + Pos vuz400 * vuz31) (vuz31 * vuz41) (primEqInt (vuz31 * vuz41) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3]; 22[label="reduce2Reduce1 (vuz30 * vuz41 + Neg vuz400 * vuz31) (primMulInt vuz31 vuz41) (vuz30 * vuz41 + Neg vuz400 * vuz31) (primMulInt vuz31 vuz41) (primEqInt (primMulInt vuz31 vuz41) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6386[label="vuz31/Pos vuz310",fontsize=10,color="white",style="solid",shape="box"];22 -> 6386[label="",style="solid", color="burlywood", weight=9]; 6386 -> 24[label="",style="solid", color="burlywood", weight=3]; 6387[label="vuz31/Neg 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weight=9]; 6392 -> 30[label="",style="solid", color="burlywood", weight=3]; 6393[label="vuz41/Neg vuz410",fontsize=10,color="white",style="solid",shape="box"];25 -> 6393[label="",style="solid", color="burlywood", weight=9]; 6393 -> 31[label="",style="solid", color="burlywood", weight=3]; 26[label="reduce2Reduce1 (vuz30 * vuz41 + Pos vuz400 * Pos vuz310) (primMulInt (Pos vuz310) vuz41) (vuz30 * vuz41 + Pos vuz400 * Pos vuz310) (primMulInt (Pos vuz310) vuz41) (primEqInt (primMulInt (Pos vuz310) vuz41) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6394[label="vuz41/Pos vuz410",fontsize=10,color="white",style="solid",shape="box"];26 -> 6394[label="",style="solid", color="burlywood", weight=9]; 6394 -> 32[label="",style="solid", color="burlywood", weight=3]; 6395[label="vuz41/Neg vuz410",fontsize=10,color="white",style="solid",shape="box"];26 -> 6395[label="",style="solid", color="burlywood", weight=9]; 6395 -> 33[label="",style="solid", color="burlywood", weight=3]; 27[label="reduce2Reduce1 (vuz30 * vuz41 + Pos vuz400 * Neg vuz310) (primMulInt (Neg vuz310) vuz41) (vuz30 * vuz41 + Pos vuz400 * Neg vuz310) (primMulInt (Neg vuz310) vuz41) (primEqInt (primMulInt (Neg vuz310) vuz41) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6396[label="vuz41/Pos vuz410",fontsize=10,color="white",style="solid",shape="box"];27 -> 6396[label="",style="solid", color="burlywood", weight=9]; 6396 -> 34[label="",style="solid", color="burlywood", weight=3]; 6397[label="vuz41/Neg vuz410",fontsize=10,color="white",style="solid",shape="box"];27 -> 6397[label="",style="solid", color="burlywood", weight=9]; 6397 -> 35[label="",style="solid", color="burlywood", weight=3]; 28[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Neg vuz400 * Pos vuz310) (primMulInt (Pos vuz310) (Pos vuz410)) (vuz30 * Pos vuz410 + Neg vuz400 * Pos vuz310) (primMulInt (Pos vuz310) (Pos vuz410)) (primEqInt (primMulInt (Pos vuz310) (Pos vuz410)) (fromInt (Pos 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6401[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];37 -> 6401[label="",style="solid", color="burlywood", weight=9]; 6401 -> 47[label="",style="solid", color="burlywood", weight=3]; 38[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Neg vuz400 * Neg vuz310) (Neg (primMulNat vuz310 vuz410)) (vuz30 * Pos vuz410 + Neg vuz400 * Neg vuz310) (Neg (primMulNat vuz310 vuz410)) (primEqInt (Neg (primMulNat vuz310 vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6402[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];38 -> 6402[label="",style="solid", color="burlywood", weight=9]; 6402 -> 48[label="",style="solid", color="burlywood", weight=3]; 6403[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];38 -> 6403[label="",style="solid", color="burlywood", weight=9]; 6403 -> 49[label="",style="solid", color="burlywood", weight=3]; 39[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Neg vuz400 * Neg vuz310) 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6409[label="",style="solid", color="burlywood", weight=9]; 6409 -> 55[label="",style="solid", color="burlywood", weight=3]; 42[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Pos vuz400 * Neg vuz310) (Neg (primMulNat vuz310 vuz410)) (vuz30 * Pos vuz410 + Pos vuz400 * Neg vuz310) (Neg (primMulNat vuz310 vuz410)) (primEqInt (Neg (primMulNat vuz310 vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6410[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];42 -> 6410[label="",style="solid", color="burlywood", weight=9]; 6410 -> 56[label="",style="solid", color="burlywood", weight=3]; 6411[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];42 -> 6411[label="",style="solid", color="burlywood", weight=9]; 6411 -> 57[label="",style="solid", color="burlywood", weight=3]; 43[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Pos vuz400 * Neg vuz310) (Pos (primMulNat vuz310 vuz410)) (vuz30 * Neg vuz410 + Pos vuz400 * Neg vuz310) (Pos 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6414[label="",style="solid", color="burlywood", weight=9]; 6414 -> 60[label="",style="solid", color="burlywood", weight=3]; 6415[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];44 -> 6415[label="",style="solid", color="burlywood", weight=9]; 6415 -> 61[label="",style="solid", color="burlywood", weight=3]; 45[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Neg vuz400 * Pos Zero) (Pos (primMulNat Zero vuz410)) (vuz30 * Pos vuz410 + Neg vuz400 * Pos Zero) (Pos (primMulNat Zero vuz410)) (primEqInt (Pos (primMulNat Zero vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6416[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];45 -> 6416[label="",style="solid", color="burlywood", weight=9]; 6416 -> 62[label="",style="solid", color="burlywood", weight=3]; 6417[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];45 -> 6417[label="",style="solid", color="burlywood", weight=9]; 6417 -> 63[label="",style="solid", color="burlywood", weight=3]; 46[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Neg vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) vuz410)) (vuz30 * Neg vuz410 + Neg vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) vuz410)) (primEqInt (Neg (primMulNat (Succ vuz3100) vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6418[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];46 -> 6418[label="",style="solid", color="burlywood", weight=9]; 6418 -> 64[label="",style="solid", color="burlywood", weight=3]; 6419[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];46 -> 6419[label="",style="solid", color="burlywood", weight=9]; 6419 -> 65[label="",style="solid", color="burlywood", weight=3]; 47[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Neg vuz400 * Pos Zero) (Neg (primMulNat Zero vuz410)) (vuz30 * Neg vuz410 + Neg vuz400 * Pos Zero) (Neg (primMulNat Zero vuz410)) 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color="burlywood", weight=9]; 6422 -> 68[label="",style="solid", color="burlywood", weight=3]; 6423[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];48 -> 6423[label="",style="solid", color="burlywood", weight=9]; 6423 -> 69[label="",style="solid", color="burlywood", weight=3]; 49[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Neg vuz400 * Neg Zero) (Neg (primMulNat Zero vuz410)) (vuz30 * Pos vuz410 + Neg vuz400 * Neg Zero) (Neg (primMulNat Zero vuz410)) (primEqInt (Neg (primMulNat Zero vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6424[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];49 -> 6424[label="",style="solid", color="burlywood", weight=9]; 6424 -> 70[label="",style="solid", color="burlywood", weight=3]; 6425[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];49 -> 6425[label="",style="solid", color="burlywood", weight=9]; 6425 -> 71[label="",style="solid", color="burlywood", weight=3]; 50[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Neg vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) vuz410)) (vuz30 * Neg vuz410 + Neg vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) vuz410)) (primEqInt (Pos (primMulNat (Succ vuz3100) vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6426[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];50 -> 6426[label="",style="solid", color="burlywood", weight=9]; 6426 -> 72[label="",style="solid", color="burlywood", weight=3]; 6427[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];50 -> 6427[label="",style="solid", color="burlywood", weight=9]; 6427 -> 73[label="",style="solid", color="burlywood", weight=3]; 51[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Neg vuz400 * Neg Zero) (Pos (primMulNat Zero vuz410)) (vuz30 * Neg vuz410 + Neg vuz400 * Neg Zero) (Pos (primMulNat Zero vuz410)) (primEqInt (Pos (primMulNat Zero vuz410)) (fromInt 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76[label="",style="solid", color="burlywood", weight=3]; 6431[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];52 -> 6431[label="",style="solid", color="burlywood", weight=9]; 6431 -> 77[label="",style="solid", color="burlywood", weight=3]; 53[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Pos vuz400 * Pos Zero) (Pos (primMulNat Zero vuz410)) (vuz30 * Pos vuz410 + Pos vuz400 * Pos Zero) (Pos (primMulNat Zero vuz410)) (primEqInt (Pos (primMulNat Zero vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6432[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];53 -> 6432[label="",style="solid", color="burlywood", weight=9]; 6432 -> 78[label="",style="solid", color="burlywood", weight=3]; 6433[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];53 -> 6433[label="",style="solid", color="burlywood", weight=9]; 6433 -> 79[label="",style="solid", color="burlywood", weight=3]; 54[label="reduce2Reduce1 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color="burlywood", weight=3]; 6439[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];56 -> 6439[label="",style="solid", color="burlywood", weight=9]; 6439 -> 85[label="",style="solid", color="burlywood", weight=3]; 57[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Pos vuz400 * Neg Zero) (Neg (primMulNat Zero vuz410)) (vuz30 * Pos vuz410 + Pos vuz400 * Neg Zero) (Neg (primMulNat Zero vuz410)) (primEqInt (Neg (primMulNat Zero vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6440[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];57 -> 6440[label="",style="solid", color="burlywood", weight=9]; 6440 -> 86[label="",style="solid", color="burlywood", weight=3]; 6441[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];57 -> 6441[label="",style="solid", color="burlywood", weight=9]; 6441 -> 87[label="",style="solid", color="burlywood", weight=3]; 58[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Pos 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64[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) (Succ vuz4100))) (primEqInt (Neg (primMulNat (Succ vuz3100) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];64 -> 96[label="",style="solid", color="black", weight=3]; 65[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) Zero)) (vuz30 * Neg Zero + Neg vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) Zero)) (primEqInt (Neg (primMulNat (Succ vuz3100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];65 -> 97[label="",style="solid", color="black", weight=3]; 66[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos Zero) (Neg (primMulNat Zero (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos Zero) (Neg (primMulNat 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103[label="",style="solid", color="black", weight=3]; 72[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) (Succ vuz4100))) (primEqInt (Pos (primMulNat (Succ vuz3100) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];72 -> 104[label="",style="solid", color="black", weight=3]; 73[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) Zero)) (vuz30 * Neg Zero + Neg vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) Zero)) (primEqInt (Pos (primMulNat (Succ vuz3100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];73 -> 105[label="",style="solid", color="black", weight=3]; 74[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg Zero) (Pos (primMulNat Zero (Succ vuz4100))) (vuz30 * Neg 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color="black", weight=3]; 90[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg Zero) (Pos (primMulNat Zero (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg Zero) (Pos (primMulNat Zero (Succ vuz4100))) (primEqInt (Pos (primMulNat Zero (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];90 -> 122[label="",style="solid", color="black", weight=3]; 91[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Neg Zero) (Pos (primMulNat Zero Zero)) (vuz30 * Neg Zero + Pos vuz400 * Neg Zero) (Pos (primMulNat Zero Zero)) (primEqInt (Pos (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];91 -> 123[label="",style="solid", color="black", weight=3]; 92 -> 1963[label="",style="dashed", color="red", weight=0]; 92[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos (Succ vuz3100)) (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos (Succ vuz3100)) (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (primEqInt (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];92 -> 1964[label="",style="dashed", color="magenta", weight=3]; 92 -> 1965[label="",style="dashed", color="magenta", weight=3]; 92 -> 1966[label="",style="dashed", color="magenta", weight=3]; 92 -> 1967[label="",style="dashed", color="magenta", weight=3]; 92 -> 1968[label="",style="dashed", color="magenta", weight=3]; 92 -> 1969[label="",style="dashed", color="magenta", weight=3]; 92 -> 1970[label="",style="dashed", color="magenta", weight=3]; 93[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Pos (Succ vuz3100)) (Pos Zero) (vuz30 * Pos Zero + Neg vuz400 * Pos (Succ vuz3100)) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];93 -> 126[label="",style="solid", color="black", weight=3]; 94[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];94 -> 127[label="",style="solid", color="black", weight=3]; 95[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos Zero + Neg vuz400 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];95 -> 128[label="",style="solid", color="black", weight=3]; 96 -> 1030[label="",style="dashed", color="red", weight=0]; 96[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos (Succ vuz3100)) (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos (Succ vuz3100)) (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (primEqInt (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];96 -> 1031[label="",style="dashed", color="magenta", weight=3]; 96 -> 1032[label="",style="dashed", color="magenta", weight=3]; 96 -> 1033[label="",style="dashed", color="magenta", weight=3]; 96 -> 1034[label="",style="dashed", color="magenta", weight=3]; 96 -> 1035[label="",style="dashed", color="magenta", weight=3]; 96 -> 1036[label="",style="dashed", color="magenta", weight=3]; 96 -> 1037[label="",style="dashed", color="magenta", weight=3]; 97[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Pos (Succ vuz3100)) (Neg Zero) (vuz30 * Neg Zero + Neg vuz400 * Pos (Succ vuz3100)) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];97 -> 131[label="",style="solid", color="black", weight=3]; 98[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];98 -> 132[label="",style="solid", color="black", weight=3]; 99[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg Zero + Neg vuz400 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];99 -> 133[label="",style="solid", color="black", weight=3]; 100 -> 1073[label="",style="dashed", color="red", weight=0]; 100[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg (Succ vuz3100)) (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg (Succ vuz3100)) (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (primEqInt (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];100 -> 1074[label="",style="dashed", color="magenta", weight=3]; 100 -> 1075[label="",style="dashed", color="magenta", weight=3]; 100 -> 1076[label="",style="dashed", color="magenta", weight=3]; 100 -> 1077[label="",style="dashed", color="magenta", weight=3]; 100 -> 1078[label="",style="dashed", color="magenta", weight=3]; 100 -> 1079[label="",style="dashed", color="magenta", weight=3]; 100 -> 1080[label="",style="dashed", color="magenta", weight=3]; 101[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Neg (Succ vuz3100)) (Neg Zero) (vuz30 * Pos Zero + Neg vuz400 * Neg (Succ vuz3100)) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];101 -> 136[label="",style="solid", color="black", weight=3]; 102[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];102 -> 137[label="",style="solid", color="black", weight=3]; 103[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos Zero + Neg vuz400 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];103 -> 138[label="",style="solid", color="black", weight=3]; 104 -> 1126[label="",style="dashed", color="red", weight=0]; 104[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg (Succ vuz3100)) (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg (Succ vuz3100)) (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (primEqInt (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];104 -> 1127[label="",style="dashed", color="magenta", weight=3]; 104 -> 1128[label="",style="dashed", color="magenta", weight=3]; 104 -> 1129[label="",style="dashed", color="magenta", weight=3]; 104 -> 1130[label="",style="dashed", color="magenta", weight=3]; 104 -> 1131[label="",style="dashed", color="magenta", weight=3]; 104 -> 1132[label="",style="dashed", color="magenta", weight=3]; 104 -> 1133[label="",style="dashed", color="magenta", weight=3]; 105[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Neg (Succ vuz3100)) (Pos Zero) (vuz30 * Neg Zero + Neg vuz400 * Neg (Succ vuz3100)) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];105 -> 141[label="",style="solid", color="black", weight=3]; 106[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];106 -> 142[label="",style="solid", color="black", weight=3]; 107[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg Zero + Neg vuz400 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];107 -> 143[label="",style="solid", color="black", weight=3]; 108 -> 1186[label="",style="dashed", color="red", weight=0]; 108[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos (Succ vuz3100)) (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos (Succ vuz3100)) (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (primEqInt (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];108 -> 1187[label="",style="dashed", color="magenta", weight=3]; 108 -> 1188[label="",style="dashed", color="magenta", weight=3]; 108 -> 1189[label="",style="dashed", color="magenta", weight=3]; 108 -> 1190[label="",style="dashed", color="magenta", weight=3]; 108 -> 1191[label="",style="dashed", color="magenta", weight=3]; 108 -> 1192[label="",style="dashed", color="magenta", weight=3]; 108 -> 1193[label="",style="dashed", color="magenta", weight=3]; 109[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Pos (Succ vuz3100)) (Pos Zero) (vuz30 * Pos Zero + Pos vuz400 * Pos (Succ vuz3100)) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];109 -> 146[label="",style="solid", color="black", weight=3]; 110[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];110 -> 147[label="",style="solid", color="black", weight=3]; 111[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos Zero + Pos vuz400 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];111 -> 148[label="",style="solid", color="black", weight=3]; 112 -> 1359[label="",style="dashed", color="red", weight=0]; 112[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos (Succ vuz3100)) (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos (Succ vuz3100)) (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (primEqInt (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];112 -> 1360[label="",style="dashed", color="magenta", weight=3]; 112 -> 1361[label="",style="dashed", color="magenta", weight=3]; 112 -> 1362[label="",style="dashed", color="magenta", weight=3]; 112 -> 1363[label="",style="dashed", color="magenta", weight=3]; 112 -> 1364[label="",style="dashed", color="magenta", weight=3]; 112 -> 1365[label="",style="dashed", color="magenta", weight=3]; 112 -> 1366[label="",style="dashed", color="magenta", weight=3]; 113[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Pos (Succ vuz3100)) (Neg Zero) (vuz30 * Neg Zero + Pos vuz400 * Pos (Succ vuz3100)) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];113 -> 151[label="",style="solid", color="black", weight=3]; 114[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];114 -> 152[label="",style="solid", color="black", weight=3]; 115[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg Zero + Pos vuz400 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];115 -> 153[label="",style="solid", color="black", weight=3]; 116 -> 1539[label="",style="dashed", color="red", weight=0]; 116[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg (Succ vuz3100)) (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg (Succ vuz3100)) (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (primEqInt (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];116 -> 1540[label="",style="dashed", color="magenta", weight=3]; 116 -> 1541[label="",style="dashed", color="magenta", weight=3]; 116 -> 1542[label="",style="dashed", color="magenta", weight=3]; 116 -> 1543[label="",style="dashed", color="magenta", weight=3]; 116 -> 1544[label="",style="dashed", color="magenta", weight=3]; 116 -> 1545[label="",style="dashed", color="magenta", weight=3]; 116 -> 1546[label="",style="dashed", color="magenta", weight=3]; 117[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Neg (Succ vuz3100)) (Neg Zero) (vuz30 * Pos Zero + Pos vuz400 * Neg (Succ vuz3100)) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];117 -> 156[label="",style="solid", color="black", weight=3]; 118[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];118 -> 157[label="",style="solid", color="black", weight=3]; 119[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos Zero + Pos vuz400 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];119 -> 158[label="",style="solid", color="black", weight=3]; 120 -> 1722[label="",style="dashed", color="red", weight=0]; 120[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg (Succ vuz3100)) (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg (Succ vuz3100)) (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (primEqInt (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];120 -> 1723[label="",style="dashed", color="magenta", weight=3]; 120 -> 1724[label="",style="dashed", color="magenta", weight=3]; 120 -> 1725[label="",style="dashed", color="magenta", weight=3]; 120 -> 1726[label="",style="dashed", color="magenta", weight=3]; 120 -> 1727[label="",style="dashed", color="magenta", weight=3]; 120 -> 1728[label="",style="dashed", color="magenta", weight=3]; 120 -> 1729[label="",style="dashed", color="magenta", weight=3]; 121[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Neg (Succ vuz3100)) (Pos Zero) (vuz30 * Neg Zero + Pos vuz400 * Neg (Succ vuz3100)) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];121 -> 161[label="",style="solid", color="black", weight=3]; 122[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];122 -> 162[label="",style="solid", color="black", weight=3]; 123[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg Zero + Pos vuz400 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];123 -> 163[label="",style="solid", color="black", weight=3]; 1964[label="vuz4100",fontsize=16,color="green",shape="box"];1965[label="vuz400",fontsize=16,color="green",shape="box"];1966 -> 1352[label="",style="dashed", color="red", weight=0]; 1966[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1966 -> 2127[label="",style="dashed", color="magenta", weight=3]; 1966 -> 2128[label="",style="dashed", color="magenta", weight=3]; 1967[label="vuz30",fontsize=16,color="green",shape="box"];1968[label="vuz3100",fontsize=16,color="green",shape="box"];1969 -> 1352[label="",style="dashed", color="red", weight=0]; 1969[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1969 -> 2129[label="",style="dashed", color="magenta", weight=3]; 1969 -> 2130[label="",style="dashed", color="magenta", weight=3]; 1970 -> 1352[label="",style="dashed", color="red", weight=0]; 1970[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1970 -> 2131[label="",style="dashed", color="magenta", weight=3]; 1970 -> 2132[label="",style="dashed", color="magenta", weight=3]; 1963[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos vuz145) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6446[label="vuz145/Succ vuz1450",fontsize=10,color="white",style="solid",shape="box"];1963 -> 6446[label="",style="solid", color="burlywood", weight=9]; 6446 -> 2133[label="",style="solid", color="burlywood", weight=3]; 6447[label="vuz145/Zero",fontsize=10,color="white",style="solid",shape="box"];1963 -> 6447[label="",style="solid", color="burlywood", weight=9]; 6447 -> 2134[label="",style="solid", color="burlywood", weight=3]; 126[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Pos (Succ vuz3100)) (Pos Zero) (vuz30 * Pos Zero + Neg vuz400 * Pos (Succ vuz3100)) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];126 -> 166[label="",style="solid", color="black", weight=3]; 127[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];127 -> 167[label="",style="solid", color="black", weight=3]; 128[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos Zero + Neg vuz400 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];128 -> 168[label="",style="solid", color="black", weight=3]; 1031[label="vuz3100",fontsize=16,color="green",shape="box"];1032 -> 1014[label="",style="dashed", color="red", weight=0]; 1032[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1032 -> 1068[label="",style="dashed", color="magenta", weight=3]; 1033[label="vuz30",fontsize=16,color="green",shape="box"];1034 -> 1014[label="",style="dashed", color="red", weight=0]; 1034[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1034 -> 1069[label="",style="dashed", color="magenta", weight=3]; 1035 -> 1014[label="",style="dashed", color="red", weight=0]; 1035[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1035 -> 1070[label="",style="dashed", color="magenta", weight=3]; 1036[label="vuz400",fontsize=16,color="green",shape="box"];1037[label="vuz4100",fontsize=16,color="green",shape="box"];1030[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg vuz69) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6448[label="vuz69/Succ vuz690",fontsize=10,color="white",style="solid",shape="box"];1030 -> 6448[label="",style="solid", color="burlywood", weight=9]; 6448 -> 1071[label="",style="solid", color="burlywood", weight=3]; 6449[label="vuz69/Zero",fontsize=10,color="white",style="solid",shape="box"];1030 -> 6449[label="",style="solid", color="burlywood", weight=9]; 6449 -> 1072[label="",style="solid", color="burlywood", weight=3]; 131[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Pos (Succ vuz3100)) (Neg Zero) (vuz30 * Neg Zero + Neg vuz400 * Pos (Succ vuz3100)) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];131 -> 171[label="",style="solid", color="black", weight=3]; 132[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];132 -> 172[label="",style="solid", color="black", weight=3]; 133[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg Zero + Neg vuz400 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];133 -> 173[label="",style="solid", color="black", weight=3]; 1074[label="vuz4100",fontsize=16,color="green",shape="box"];1075[label="vuz30",fontsize=16,color="green",shape="box"];1076 -> 1014[label="",style="dashed", color="red", weight=0]; 1076[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1076 -> 1111[label="",style="dashed", color="magenta", weight=3]; 1076 -> 1112[label="",style="dashed", color="magenta", weight=3]; 1077[label="vuz3100",fontsize=16,color="green",shape="box"];1078[label="vuz400",fontsize=16,color="green",shape="box"];1079 -> 1014[label="",style="dashed", color="red", weight=0]; 1079[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1079 -> 1113[label="",style="dashed", color="magenta", weight=3]; 1079 -> 1114[label="",style="dashed", color="magenta", weight=3]; 1080 -> 1014[label="",style="dashed", color="red", weight=0]; 1080[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1080 -> 1115[label="",style="dashed", color="magenta", weight=3]; 1080 -> 1116[label="",style="dashed", color="magenta", weight=3]; 1073[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg vuz72) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6450[label="vuz72/Succ vuz720",fontsize=10,color="white",style="solid",shape="box"];1073 -> 6450[label="",style="solid", color="burlywood", weight=9]; 6450 -> 1117[label="",style="solid", color="burlywood", weight=3]; 6451[label="vuz72/Zero",fontsize=10,color="white",style="solid",shape="box"];1073 -> 6451[label="",style="solid", color="burlywood", weight=9]; 6451 -> 1118[label="",style="solid", color="burlywood", weight=3]; 136[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Neg (Succ vuz3100)) (Neg Zero) (vuz30 * Pos Zero + Neg vuz400 * Neg (Succ vuz3100)) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];136 -> 176[label="",style="solid", color="black", weight=3]; 137[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];137 -> 177[label="",style="solid", color="black", weight=3]; 138[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos Zero + Neg vuz400 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];138 -> 178[label="",style="solid", color="black", weight=3]; 1127[label="vuz30",fontsize=16,color="green",shape="box"];1128[label="vuz4100",fontsize=16,color="green",shape="box"];1129[label="vuz400",fontsize=16,color="green",shape="box"];1130 -> 1014[label="",style="dashed", color="red", weight=0]; 1130[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1130 -> 1164[label="",style="dashed", color="magenta", weight=3]; 1131 -> 1014[label="",style="dashed", color="red", weight=0]; 1131[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1131 -> 1165[label="",style="dashed", color="magenta", weight=3]; 1132 -> 1014[label="",style="dashed", color="red", weight=0]; 1132[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1132 -> 1166[label="",style="dashed", color="magenta", weight=3]; 1133[label="vuz3100",fontsize=16,color="green",shape="box"];1126[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos vuz75) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6452[label="vuz75/Succ vuz750",fontsize=10,color="white",style="solid",shape="box"];1126 -> 6452[label="",style="solid", color="burlywood", weight=9]; 6452 -> 1167[label="",style="solid", color="burlywood", weight=3]; 6453[label="vuz75/Zero",fontsize=10,color="white",style="solid",shape="box"];1126 -> 6453[label="",style="solid", color="burlywood", weight=9]; 6453 -> 1168[label="",style="solid", color="burlywood", weight=3]; 141[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Neg (Succ vuz3100)) (Pos Zero) (vuz30 * Neg Zero + Neg vuz400 * Neg (Succ vuz3100)) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];141 -> 181[label="",style="solid", color="black", weight=3]; 142[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];142 -> 182[label="",style="solid", color="black", weight=3]; 143[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg Zero + Neg vuz400 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];143 -> 183[label="",style="solid", color="black", weight=3]; 1187[label="vuz400",fontsize=16,color="green",shape="box"];1188[label="vuz30",fontsize=16,color="green",shape="box"];1189 -> 1014[label="",style="dashed", color="red", weight=0]; 1189[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1189 -> 1337[label="",style="dashed", color="magenta", weight=3]; 1189 -> 1338[label="",style="dashed", color="magenta", weight=3]; 1190 -> 1014[label="",style="dashed", color="red", weight=0]; 1190[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1190 -> 1339[label="",style="dashed", color="magenta", weight=3]; 1190 -> 1340[label="",style="dashed", color="magenta", weight=3]; 1191[label="vuz3100",fontsize=16,color="green",shape="box"];1192[label="vuz4100",fontsize=16,color="green",shape="box"];1193 -> 1014[label="",style="dashed", color="red", weight=0]; 1193[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1193 -> 1341[label="",style="dashed", color="magenta", weight=3]; 1193 -> 1342[label="",style="dashed", color="magenta", weight=3]; 1186[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos vuz78) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6454[label="vuz78/Succ vuz780",fontsize=10,color="white",style="solid",shape="box"];1186 -> 6454[label="",style="solid", color="burlywood", weight=9]; 6454 -> 1343[label="",style="solid", color="burlywood", weight=3]; 6455[label="vuz78/Zero",fontsize=10,color="white",style="solid",shape="box"];1186 -> 6455[label="",style="solid", color="burlywood", weight=9]; 6455 -> 1344[label="",style="solid", color="burlywood", weight=3]; 146[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Pos (Succ vuz3100)) (Pos Zero) (vuz30 * Pos Zero + Pos vuz400 * Pos (Succ vuz3100)) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];146 -> 186[label="",style="solid", color="black", weight=3]; 147[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];147 -> 187[label="",style="solid", color="black", weight=3]; 148[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos Zero + Pos vuz400 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];148 -> 188[label="",style="solid", color="black", weight=3]; 1360[label="vuz30",fontsize=16,color="green",shape="box"];1361[label="vuz4100",fontsize=16,color="green",shape="box"];1362 -> 1014[label="",style="dashed", color="red", weight=0]; 1362[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1362 -> 1517[label="",style="dashed", color="magenta", weight=3]; 1363 -> 1014[label="",style="dashed", color="red", weight=0]; 1363[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1363 -> 1518[label="",style="dashed", color="magenta", weight=3]; 1364[label="vuz400",fontsize=16,color="green",shape="box"];1365 -> 1014[label="",style="dashed", color="red", weight=0]; 1365[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1365 -> 1519[label="",style="dashed", color="magenta", weight=3]; 1366[label="vuz3100",fontsize=16,color="green",shape="box"];1359[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg vuz93) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6456[label="vuz93/Succ vuz930",fontsize=10,color="white",style="solid",shape="box"];1359 -> 6456[label="",style="solid", color="burlywood", weight=9]; 6456 -> 1520[label="",style="solid", color="burlywood", weight=3]; 6457[label="vuz93/Zero",fontsize=10,color="white",style="solid",shape="box"];1359 -> 6457[label="",style="solid", color="burlywood", weight=9]; 6457 -> 1521[label="",style="solid", color="burlywood", weight=3]; 151[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Pos (Succ vuz3100)) (Neg Zero) (vuz30 * Neg Zero + Pos vuz400 * Pos (Succ vuz3100)) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];151 -> 191[label="",style="solid", color="black", weight=3]; 152[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];152 -> 192[label="",style="solid", color="black", weight=3]; 153[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg Zero + Pos vuz400 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];153 -> 193[label="",style="solid", color="black", weight=3]; 1540[label="vuz4100",fontsize=16,color="green",shape="box"];1541 -> 1352[label="",style="dashed", color="red", weight=0]; 1541[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1541 -> 1697[label="",style="dashed", color="magenta", weight=3]; 1541 -> 1698[label="",style="dashed", color="magenta", weight=3]; 1542[label="vuz30",fontsize=16,color="green",shape="box"];1543[label="vuz3100",fontsize=16,color="green",shape="box"];1544 -> 1352[label="",style="dashed", color="red", weight=0]; 1544[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1544 -> 1699[label="",style="dashed", color="magenta", weight=3]; 1544 -> 1700[label="",style="dashed", color="magenta", weight=3]; 1545[label="vuz400",fontsize=16,color="green",shape="box"];1546 -> 1352[label="",style="dashed", color="red", weight=0]; 1546[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1546 -> 1701[label="",style="dashed", color="magenta", weight=3]; 1546 -> 1702[label="",style="dashed", color="magenta", weight=3]; 1539[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg vuz108) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6458[label="vuz108/Succ vuz1080",fontsize=10,color="white",style="solid",shape="box"];1539 -> 6458[label="",style="solid", color="burlywood", weight=9]; 6458 -> 1703[label="",style="solid", color="burlywood", weight=3]; 6459[label="vuz108/Zero",fontsize=10,color="white",style="solid",shape="box"];1539 -> 6459[label="",style="solid", color="burlywood", weight=9]; 6459 -> 1704[label="",style="solid", color="burlywood", weight=3]; 156[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Neg (Succ vuz3100)) (Neg Zero) (vuz30 * Pos Zero + Pos vuz400 * Neg (Succ vuz3100)) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];156 -> 196[label="",style="solid", color="black", weight=3]; 157[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];157 -> 197[label="",style="solid", color="black", weight=3]; 158[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos Zero + Pos vuz400 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];158 -> 198[label="",style="solid", color="black", weight=3]; 1723[label="vuz4100",fontsize=16,color="green",shape="box"];1724[label="vuz400",fontsize=16,color="green",shape="box"];1725 -> 1352[label="",style="dashed", color="red", weight=0]; 1725[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1725 -> 1873[label="",style="dashed", color="magenta", weight=3]; 1725 -> 1874[label="",style="dashed", color="magenta", weight=3]; 1726[label="vuz3100",fontsize=16,color="green",shape="box"];1727 -> 1352[label="",style="dashed", color="red", weight=0]; 1727[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1727 -> 1875[label="",style="dashed", color="magenta", weight=3]; 1727 -> 1876[label="",style="dashed", color="magenta", weight=3]; 1728[label="vuz30",fontsize=16,color="green",shape="box"];1729 -> 1352[label="",style="dashed", color="red", weight=0]; 1729[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1729 -> 1877[label="",style="dashed", color="magenta", weight=3]; 1729 -> 1878[label="",style="dashed", color="magenta", weight=3]; 1722[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos vuz123) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6460[label="vuz123/Succ vuz1230",fontsize=10,color="white",style="solid",shape="box"];1722 -> 6460[label="",style="solid", color="burlywood", weight=9]; 6460 -> 1879[label="",style="solid", color="burlywood", weight=3]; 6461[label="vuz123/Zero",fontsize=10,color="white",style="solid",shape="box"];1722 -> 6461[label="",style="solid", color="burlywood", weight=9]; 6461 -> 1880[label="",style="solid", color="burlywood", weight=3]; 161[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Neg (Succ vuz3100)) (Pos Zero) (vuz30 * Neg Zero + Pos vuz400 * Neg (Succ vuz3100)) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];161 -> 201[label="",style="solid", color="black", weight=3]; 162[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];162 -> 202[label="",style="solid", color="black", weight=3]; 163[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg Zero + Pos vuz400 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];163 -> 203[label="",style="solid", color="black", weight=3]; 2127[label="Succ vuz4100",fontsize=16,color="green",shape="box"];2128 -> 678[label="",style="dashed", color="red", weight=0]; 2128[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];2128 -> 2147[label="",style="dashed", color="magenta", weight=3]; 2128 -> 2148[label="",style="dashed", color="magenta", weight=3]; 1352[label="primPlusNat vuz660 vuz4100",fontsize=16,color="burlywood",shape="triangle"];6462[label="vuz660/Succ vuz6600",fontsize=10,color="white",style="solid",shape="box"];1352 -> 6462[label="",style="solid", color="burlywood", weight=9]; 6462 -> 1534[label="",style="solid", color="burlywood", weight=3]; 6463[label="vuz660/Zero",fontsize=10,color="white",style="solid",shape="box"];1352 -> 6463[label="",style="solid", color="burlywood", weight=9]; 6463 -> 1535[label="",style="solid", color="burlywood", weight=3]; 2129[label="Succ vuz4100",fontsize=16,color="green",shape="box"];2130 -> 678[label="",style="dashed", color="red", weight=0]; 2130[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];2130 -> 2149[label="",style="dashed", color="magenta", weight=3]; 2130 -> 2150[label="",style="dashed", color="magenta", weight=3]; 2131[label="Succ vuz4100",fontsize=16,color="green",shape="box"];2132 -> 678[label="",style="dashed", color="red", weight=0]; 2132[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];2132 -> 2151[label="",style="dashed", color="magenta", weight=3]; 2132 -> 2152[label="",style="dashed", color="magenta", weight=3]; 2133[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos (Succ vuz1450)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];2133 -> 2153[label="",style="solid", color="black", weight=3]; 2134[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];2134 -> 2154[label="",style="solid", color="black", weight=3]; 166[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Pos (Succ vuz3100)) (Pos Zero) (vuz30 * Pos Zero + Neg vuz400 * Pos (Succ vuz3100)) (Pos Zero) True",fontsize=16,color="black",shape="box"];166 -> 207[label="",style="solid", color="black", weight=3]; 167[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];167 -> 208[label="",style="solid", color="black", weight=3]; 168[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos Zero + Neg vuz400 * Pos Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];168 -> 209[label="",style="solid", color="black", weight=3]; 1068 -> 678[label="",style="dashed", color="red", weight=0]; 1068[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1068 -> 1119[label="",style="dashed", color="magenta", weight=3]; 1014[label="primPlusNat vuz66 (Succ vuz4100)",fontsize=16,color="burlywood",shape="triangle"];6464[label="vuz66/Succ vuz660",fontsize=10,color="white",style="solid",shape="box"];1014 -> 6464[label="",style="solid", color="burlywood", weight=9]; 6464 -> 1120[label="",style="solid", color="burlywood", weight=3]; 6465[label="vuz66/Zero",fontsize=10,color="white",style="solid",shape="box"];1014 -> 6465[label="",style="solid", color="burlywood", weight=9]; 6465 -> 1121[label="",style="solid", color="burlywood", weight=3]; 1069 -> 678[label="",style="dashed", color="red", weight=0]; 1069[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1069 -> 1122[label="",style="dashed", color="magenta", weight=3]; 1070 -> 678[label="",style="dashed", color="red", weight=0]; 1070[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1070 -> 1123[label="",style="dashed", color="magenta", weight=3]; 1071[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg (Succ vuz690)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1071 -> 1124[label="",style="solid", color="black", weight=3]; 1072[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1072 -> 1125[label="",style="solid", color="black", weight=3]; 171[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Pos (Succ vuz3100)) (Neg Zero) (vuz30 * Neg Zero + Neg vuz400 * Pos (Succ vuz3100)) (Neg Zero) True",fontsize=16,color="black",shape="box"];171 -> 213[label="",style="solid", color="black", weight=3]; 172[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];172 -> 214[label="",style="solid", color="black", weight=3]; 173[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg Zero + Neg vuz400 * Pos Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];173 -> 215[label="",style="solid", color="black", weight=3]; 1111 -> 678[label="",style="dashed", color="red", weight=0]; 1111[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1111 -> 1169[label="",style="dashed", color="magenta", weight=3]; 1111 -> 1170[label="",style="dashed", color="magenta", weight=3]; 1112[label="vuz4100",fontsize=16,color="green",shape="box"];1113 -> 678[label="",style="dashed", color="red", weight=0]; 1113[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1113 -> 1171[label="",style="dashed", color="magenta", weight=3]; 1113 -> 1172[label="",style="dashed", color="magenta", weight=3]; 1114[label="vuz4100",fontsize=16,color="green",shape="box"];1115 -> 678[label="",style="dashed", color="red", weight=0]; 1115[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1115 -> 1173[label="",style="dashed", color="magenta", weight=3]; 1115 -> 1174[label="",style="dashed", color="magenta", weight=3]; 1116[label="vuz4100",fontsize=16,color="green",shape="box"];1117[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * 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220[label="",style="solid", color="black", weight=3]; 178[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos Zero + Neg vuz400 * Neg Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];178 -> 221[label="",style="solid", color="black", weight=3]; 1164 -> 678[label="",style="dashed", color="red", weight=0]; 1164[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1164 -> 1345[label="",style="dashed", color="magenta", weight=3]; 1165 -> 678[label="",style="dashed", color="red", weight=0]; 1165[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1165 -> 1346[label="",style="dashed", color="magenta", weight=3]; 1166 -> 678[label="",style="dashed", color="red", weight=0]; 1166[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1166 -> 1347[label="",style="dashed", color="magenta", weight=3]; 1167[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos (Succ vuz750)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1167 -> 1348[label="",style="solid", color="black", weight=3]; 1168[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1168 -> 1349[label="",style="solid", color="black", weight=3]; 181[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Neg (Succ vuz3100)) (Pos Zero) (vuz30 * Neg Zero + Neg vuz400 * Neg (Succ vuz3100)) (Pos Zero) True",fontsize=16,color="black",shape="box"];181 -> 225[label="",style="solid", color="black", weight=3]; 182[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];182 -> 226[label="",style="solid", color="black", weight=3]; 183[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg Zero + Neg vuz400 * Neg Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];183 -> 227[label="",style="solid", color="black", weight=3]; 1337 -> 678[label="",style="dashed", color="red", weight=0]; 1337[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1337 -> 1522[label="",style="dashed", color="magenta", weight=3]; 1337 -> 1523[label="",style="dashed", color="magenta", weight=3]; 1338[label="vuz4100",fontsize=16,color="green",shape="box"];1339 -> 678[label="",style="dashed", color="red", weight=0]; 1339[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1339 -> 1524[label="",style="dashed", color="magenta", weight=3]; 1339 -> 1525[label="",style="dashed", color="magenta", weight=3]; 1340[label="vuz4100",fontsize=16,color="green",shape="box"];1341 -> 678[label="",style="dashed", color="red", weight=0]; 1341[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1341 -> 1526[label="",style="dashed", color="magenta", weight=3]; 1341 -> 1527[label="",style="dashed", color="magenta", weight=3]; 1342[label="vuz4100",fontsize=16,color="green",shape="box"];1343[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos (Succ vuz780)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1343 -> 1528[label="",style="solid", color="black", weight=3]; 1344[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1344 -> 1529[label="",style="solid", color="black", weight=3]; 186[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Pos (Succ vuz3100)) (Pos Zero) (vuz30 * Pos Zero + Pos vuz400 * Pos (Succ vuz3100)) (Pos Zero) True",fontsize=16,color="black",shape="box"];186 -> 231[label="",style="solid", color="black", weight=3]; 187[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];187 -> 232[label="",style="solid", color="black", weight=3]; 188[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos Zero + Pos vuz400 * Pos Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];188 -> 233[label="",style="solid", color="black", weight=3]; 1517 -> 678[label="",style="dashed", color="red", weight=0]; 1517[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1517 -> 1705[label="",style="dashed", color="magenta", weight=3]; 1518 -> 678[label="",style="dashed", color="red", weight=0]; 1518[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1518 -> 1706[label="",style="dashed", color="magenta", weight=3]; 1519 -> 678[label="",style="dashed", color="red", weight=0]; 1519[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1519 -> 1707[label="",style="dashed", color="magenta", weight=3]; 1520[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg (Succ vuz930)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1520 -> 1708[label="",style="solid", color="black", weight=3]; 1521[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1521 -> 1709[label="",style="solid", color="black", weight=3]; 191[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Pos (Succ vuz3100)) (Neg Zero) (vuz30 * Neg Zero + Pos vuz400 * Pos (Succ vuz3100)) (Neg Zero) True",fontsize=16,color="black",shape="box"];191 -> 237[label="",style="solid", color="black", weight=3]; 192[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];192 -> 238[label="",style="solid", color="black", weight=3]; 193[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg Zero + Pos vuz400 * Pos Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];193 -> 239[label="",style="solid", color="black", weight=3]; 1697[label="Succ vuz4100",fontsize=16,color="green",shape="box"];1698 -> 678[label="",style="dashed", color="red", weight=0]; 1698[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1698 -> 1881[label="",style="dashed", color="magenta", weight=3]; 1698 -> 1882[label="",style="dashed", color="magenta", weight=3]; 1699[label="Succ vuz4100",fontsize=16,color="green",shape="box"];1700 -> 678[label="",style="dashed", color="red", weight=0]; 1700[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1700 -> 1883[label="",style="dashed", color="magenta", weight=3]; 1700 -> 1884[label="",style="dashed", color="magenta", weight=3]; 1701[label="Succ vuz4100",fontsize=16,color="green",shape="box"];1702 -> 678[label="",style="dashed", color="red", weight=0]; 1702[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1702 -> 1885[label="",style="dashed", color="magenta", weight=3]; 1702 -> 1886[label="",style="dashed", color="magenta", weight=3]; 1703[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg (Succ vuz1080)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1703 -> 1887[label="",style="solid", color="black", weight=3]; 1704[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1704 -> 1888[label="",style="solid", color="black", weight=3]; 196[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Neg (Succ vuz3100)) (Neg Zero) (vuz30 * Pos Zero + Pos vuz400 * Neg (Succ vuz3100)) (Neg Zero) True",fontsize=16,color="black",shape="box"];196 -> 243[label="",style="solid", color="black", weight=3]; 197[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];197 -> 244[label="",style="solid", color="black", weight=3]; 198[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos Zero + Pos vuz400 * Neg Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];198 -> 245[label="",style="solid", color="black", weight=3]; 1873[label="Succ vuz4100",fontsize=16,color="green",shape="box"];1874 -> 678[label="",style="dashed", color="red", weight=0]; 1874[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1874 -> 1915[label="",style="dashed", color="magenta", weight=3]; 1875[label="Succ vuz4100",fontsize=16,color="green",shape="box"];1876 -> 678[label="",style="dashed", color="red", weight=0]; 1876[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1876 -> 1916[label="",style="dashed", color="magenta", weight=3]; 1877[label="Succ vuz4100",fontsize=16,color="green",shape="box"];1878 -> 678[label="",style="dashed", color="red", weight=0]; 1878[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1878 -> 1917[label="",style="dashed", color="magenta", weight=3]; 1879[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos (Succ vuz1230)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1879 -> 1918[label="",style="solid", color="black", weight=3]; 1880[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1880 -> 1919[label="",style="solid", color="black", weight=3]; 201[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Neg (Succ vuz3100)) (Pos Zero) (vuz30 * Neg Zero + Pos vuz400 * Neg (Succ vuz3100)) (Pos Zero) True",fontsize=16,color="black",shape="box"];201 -> 249[label="",style="solid", color="black", weight=3]; 202[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];202 -> 250[label="",style="solid", color="black", weight=3]; 203[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg Zero + Pos vuz400 * Neg Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];203 -> 251[label="",style="solid", color="black", weight=3]; 2147[label="vuz3100",fontsize=16,color="green",shape="box"];2148[label="vuz4100",fontsize=16,color="green",shape="box"];678[label="primMulNat vuz31000 (Succ vuz4100)",fontsize=16,color="burlywood",shape="triangle"];6466[label="vuz31000/Succ vuz310000",fontsize=10,color="white",style="solid",shape="box"];678 -> 6466[label="",style="solid", color="burlywood", weight=9]; 6466 -> 779[label="",style="solid", color="burlywood", weight=3]; 6467[label="vuz31000/Zero",fontsize=10,color="white",style="solid",shape="box"];678 -> 6467[label="",style="solid", color="burlywood", weight=9]; 6467 -> 780[label="",style="solid", color="burlywood", weight=3]; 1534[label="primPlusNat (Succ vuz6600) vuz4100",fontsize=16,color="burlywood",shape="box"];6468[label="vuz4100/Succ vuz41000",fontsize=10,color="white",style="solid",shape="box"];1534 -> 6468[label="",style="solid", color="burlywood", weight=9]; 6468 -> 1715[label="",style="solid", color="burlywood", weight=3]; 6469[label="vuz4100/Zero",fontsize=10,color="white",style="solid",shape="box"];1534 -> 6469[label="",style="solid", color="burlywood", weight=9]; 6469 -> 1716[label="",style="solid", color="burlywood", weight=3]; 1535[label="primPlusNat Zero vuz4100",fontsize=16,color="burlywood",shape="box"];6470[label="vuz4100/Succ vuz41000",fontsize=10,color="white",style="solid",shape="box"];1535 -> 6470[label="",style="solid", color="burlywood", weight=9]; 6470 -> 1717[label="",style="solid", color="burlywood", weight=3]; 6471[label="vuz4100/Zero",fontsize=10,color="white",style="solid",shape="box"];1535 -> 6471[label="",style="solid", color="burlywood", weight=9]; 6471 -> 1718[label="",style="solid", color="burlywood", weight=3]; 2149[label="vuz3100",fontsize=16,color="green",shape="box"];2150[label="vuz4100",fontsize=16,color="green",shape="box"];2151[label="vuz3100",fontsize=16,color="green",shape="box"];2152[label="vuz4100",fontsize=16,color="green",shape="box"];2153[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos (Succ vuz1450)) (Pos Zero))",fontsize=16,color="black",shape="box"];2153 -> 2168[label="",style="solid", color="black", weight=3]; 2154[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];2154 -> 2169[label="",style="solid", color="black", weight=3]; 207[label="error []",fontsize=16,color="black",shape="triangle"];207 -> 255[label="",style="solid", color="black", weight=3]; 208 -> 207[label="",style="dashed", color="red", weight=0]; 208[label="error []",fontsize=16,color="magenta"];209 -> 207[label="",style="dashed", color="red", weight=0]; 209[label="error []",fontsize=16,color="magenta"];1119[label="vuz3100",fontsize=16,color="green",shape="box"];1120[label="primPlusNat (Succ vuz660) (Succ vuz4100)",fontsize=16,color="black",shape="box"];1120 -> 1177[label="",style="solid", color="black", weight=3]; 1121[label="primPlusNat Zero (Succ vuz4100)",fontsize=16,color="black",shape="box"];1121 -> 1178[label="",style="solid", color="black", weight=3]; 1122[label="vuz3100",fontsize=16,color="green",shape="box"];1123[label="vuz3100",fontsize=16,color="green",shape="box"];1124[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg 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[]",fontsize=16,color="magenta"];1169[label="vuz3100",fontsize=16,color="green",shape="box"];1170[label="vuz4100",fontsize=16,color="green",shape="box"];1171[label="vuz3100",fontsize=16,color="green",shape="box"];1172[label="vuz4100",fontsize=16,color="green",shape="box"];1173[label="vuz3100",fontsize=16,color="green",shape="box"];1174[label="vuz4100",fontsize=16,color="green",shape="box"];1175[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg (Succ vuz720)) (Pos Zero))",fontsize=16,color="black",shape="box"];1175 -> 1350[label="",style="solid", color="black", weight=3]; 1176[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1176 -> 1351[label="",style="solid", color="black", weight=3]; 219 -> 207[label="",style="dashed", color="red", weight=0]; 219[label="error []",fontsize=16,color="magenta"];220 -> 207[label="",style="dashed", color="red", weight=0]; 220[label="error []",fontsize=16,color="magenta"];221 -> 207[label="",style="dashed", color="red", weight=0]; 221[label="error []",fontsize=16,color="magenta"];1345[label="vuz3100",fontsize=16,color="green",shape="box"];1346[label="vuz3100",fontsize=16,color="green",shape="box"];1347[label="vuz3100",fontsize=16,color="green",shape="box"];1348[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos (Succ vuz750)) (Pos Zero))",fontsize=16,color="black",shape="box"];1348 -> 1530[label="",style="solid", color="black", weight=3]; 1349[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1349 -> 1531[label="",style="solid", color="black", weight=3]; 225 -> 207[label="",style="dashed", color="red", weight=0]; 225[label="error []",fontsize=16,color="magenta"];226 -> 207[label="",style="dashed", color="red", weight=0]; 226[label="error []",fontsize=16,color="magenta"];227 -> 207[label="",style="dashed", color="red", weight=0]; 227[label="error []",fontsize=16,color="magenta"];1522[label="vuz3100",fontsize=16,color="green",shape="box"];1523[label="vuz4100",fontsize=16,color="green",shape="box"];1524[label="vuz3100",fontsize=16,color="green",shape="box"];1525[label="vuz4100",fontsize=16,color="green",shape="box"];1526[label="vuz3100",fontsize=16,color="green",shape="box"];1527[label="vuz4100",fontsize=16,color="green",shape="box"];1528[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos (Succ vuz780)) (Pos Zero))",fontsize=16,color="black",shape="box"];1528 -> 1710[label="",style="solid", color="black", weight=3]; 1529[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1529 -> 1711[label="",style="solid", color="black", weight=3]; 231 -> 207[label="",style="dashed", color="red", weight=0]; 231[label="error []",fontsize=16,color="magenta"];232 -> 207[label="",style="dashed", color="red", weight=0]; 232[label="error []",fontsize=16,color="magenta"];233 -> 207[label="",style="dashed", color="red", weight=0]; 233[label="error []",fontsize=16,color="magenta"];1705[label="vuz3100",fontsize=16,color="green",shape="box"];1706[label="vuz3100",fontsize=16,color="green",shape="box"];1707[label="vuz3100",fontsize=16,color="green",shape="box"];1708[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg (Succ vuz930)) (Pos Zero))",fontsize=16,color="black",shape="box"];1708 -> 1889[label="",style="solid", color="black", weight=3]; 1709[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1709 -> 1890[label="",style="solid", color="black", weight=3]; 237 -> 207[label="",style="dashed", color="red", weight=0]; 237[label="error []",fontsize=16,color="magenta"];238 -> 207[label="",style="dashed", color="red", weight=0]; 238[label="error []",fontsize=16,color="magenta"];239 -> 207[label="",style="dashed", color="red", weight=0]; 239[label="error []",fontsize=16,color="magenta"];1881[label="vuz3100",fontsize=16,color="green",shape="box"];1882[label="vuz4100",fontsize=16,color="green",shape="box"];1883[label="vuz3100",fontsize=16,color="green",shape="box"];1884[label="vuz4100",fontsize=16,color="green",shape="box"];1885[label="vuz3100",fontsize=16,color="green",shape="box"];1886[label="vuz4100",fontsize=16,color="green",shape="box"];1887[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg (Succ vuz1080)) (Pos Zero))",fontsize=16,color="black",shape="box"];1887 -> 1920[label="",style="solid", color="black", weight=3]; 1888[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1888 -> 1921[label="",style="solid", color="black", weight=3]; 243 -> 207[label="",style="dashed", color="red", weight=0]; 243[label="error []",fontsize=16,color="magenta"];244 -> 207[label="",style="dashed", color="red", weight=0]; 244[label="error []",fontsize=16,color="magenta"];245 -> 207[label="",style="dashed", color="red", weight=0]; 245[label="error []",fontsize=16,color="magenta"];1915[label="vuz3100",fontsize=16,color="green",shape="box"];1916[label="vuz3100",fontsize=16,color="green",shape="box"];1917[label="vuz3100",fontsize=16,color="green",shape="box"];1918[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos (Succ vuz1230)) (Pos Zero))",fontsize=16,color="black",shape="box"];1918 -> 1940[label="",style="solid", color="black", weight=3]; 1919[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1919 -> 1941[label="",style="solid", color="black", weight=3]; 249 -> 207[label="",style="dashed", color="red", weight=0]; 249[label="error []",fontsize=16,color="magenta"];250 -> 207[label="",style="dashed", color="red", weight=0]; 250[label="error []",fontsize=16,color="magenta"];251 -> 207[label="",style="dashed", color="red", weight=0]; 251[label="error []",fontsize=16,color="magenta"];779[label="primMulNat (Succ vuz310000) (Succ vuz4100)",fontsize=16,color="black",shape="box"];779 -> 897[label="",style="solid", color="black", weight=3]; 780[label="primMulNat Zero (Succ vuz4100)",fontsize=16,color="black",shape="box"];780 -> 898[label="",style="solid", color="black", weight=3]; 1715[label="primPlusNat (Succ vuz6600) (Succ vuz41000)",fontsize=16,color="black",shape="box"];1715 -> 1893[label="",style="solid", color="black", weight=3]; 1716[label="primPlusNat (Succ vuz6600) Zero",fontsize=16,color="black",shape="box"];1716 -> 1894[label="",style="solid", color="black", weight=3]; 1717[label="primPlusNat Zero (Succ vuz41000)",fontsize=16,color="black",shape="box"];1717 -> 1895[label="",style="solid", color="black", weight=3]; 1718[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];1718 -> 1896[label="",style="solid", color="black", weight=3]; 2168[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) False",fontsize=16,color="black",shape="box"];2168 -> 2185[label="",style="solid", color="black", weight=3]; 2169[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) True",fontsize=16,color="black",shape="box"];2169 -> 2186[label="",style="solid", color="black", weight=3]; 255[label="error []",fontsize=16,color="red",shape="box"];1177[label="Succ (Succ (primPlusNat vuz660 vuz4100))",fontsize=16,color="green",shape="box"];1177 -> 1352[label="",style="dashed", color="green", weight=3]; 1178[label="Succ vuz4100",fontsize=16,color="green",shape="box"];1179[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) False",fontsize=16,color="black",shape="box"];1179 -> 1353[label="",style="solid", color="black", weight=3]; 1180[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) True",fontsize=16,color="black",shape="box"];1180 -> 1354[label="",style="solid", color="black", weight=3]; 1350[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) False",fontsize=16,color="black",shape="box"];1350 -> 1532[label="",style="solid", color="black", weight=3]; 1351[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) True",fontsize=16,color="black",shape="box"];1351 -> 1533[label="",style="solid", color="black", weight=3]; 1530[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) False",fontsize=16,color="black",shape="box"];1530 -> 1712[label="",style="solid", color="black", weight=3]; 1531[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) True",fontsize=16,color="black",shape="box"];1531 -> 1713[label="",style="solid", color="black", weight=3]; 1710[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) False",fontsize=16,color="black",shape="box"];1710 -> 1891[label="",style="solid", color="black", weight=3]; 1711[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) True",fontsize=16,color="black",shape="box"];1711 -> 1892[label="",style="solid", color="black", weight=3]; 1889[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) False",fontsize=16,color="black",shape="box"];1889 -> 1922[label="",style="solid", color="black", weight=3]; 1890[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) True",fontsize=16,color="black",shape="box"];1890 -> 1923[label="",style="solid", color="black", weight=3]; 1920[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) False",fontsize=16,color="black",shape="box"];1920 -> 1942[label="",style="solid", color="black", weight=3]; 1921[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) True",fontsize=16,color="black",shape="box"];1921 -> 1943[label="",style="solid", color="black", weight=3]; 1940[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) False",fontsize=16,color="black",shape="box"];1940 -> 2135[label="",style="solid", color="black", weight=3]; 1941[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) True",fontsize=16,color="black",shape="box"];1941 -> 2136[label="",style="solid", color="black", weight=3]; 897 -> 1014[label="",style="dashed", color="red", weight=0]; 897[label="primPlusNat (primMulNat vuz310000 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];897 -> 1015[label="",style="dashed", color="magenta", weight=3]; 898[label="Zero",fontsize=16,color="green",shape="box"];1893[label="Succ (Succ (primPlusNat vuz6600 vuz41000))",fontsize=16,color="green",shape="box"];1893 -> 1925[label="",style="dashed", color="green", weight=3]; 1894[label="Succ vuz6600",fontsize=16,color="green",shape="box"];1895[label="Succ vuz41000",fontsize=16,color="green",shape="box"];1896[label="Zero",fontsize=16,color="green",shape="box"];2185[label="reduce2Reduce0 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) otherwise",fontsize=16,color="black",shape="box"];2185 -> 2204[label="",style="solid", color="black", weight=3]; 2186 -> 207[label="",style="dashed", color="red", weight=0]; 2186[label="error []",fontsize=16,color="magenta"];1353[label="reduce2Reduce0 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) otherwise",fontsize=16,color="black",shape="box"];1353 -> 1536[label="",style="solid", color="black", weight=3]; 1354 -> 207[label="",style="dashed", color="red", weight=0]; 1354[label="error []",fontsize=16,color="magenta"];1532[label="reduce2Reduce0 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) otherwise",fontsize=16,color="black",shape="box"];1532 -> 1714[label="",style="solid", color="black", weight=3]; 1533 -> 207[label="",style="dashed", color="red", weight=0]; 1533[label="error []",fontsize=16,color="magenta"];1712[label="reduce2Reduce0 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) otherwise",fontsize=16,color="black",shape="box"];1712 -> 1897[label="",style="solid", color="black", weight=3]; 1713 -> 207[label="",style="dashed", color="red", weight=0]; 1713[label="error []",fontsize=16,color="magenta"];1891[label="reduce2Reduce0 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) otherwise",fontsize=16,color="black",shape="box"];1891 -> 1924[label="",style="solid", color="black", weight=3]; 1892 -> 207[label="",style="dashed", color="red", weight=0]; 1892[label="error []",fontsize=16,color="magenta"];1922[label="reduce2Reduce0 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) otherwise",fontsize=16,color="black",shape="box"];1922 -> 1944[label="",style="solid", color="black", weight=3]; 1923 -> 207[label="",style="dashed", color="red", weight=0]; 1923[label="error []",fontsize=16,color="magenta"];1942[label="reduce2Reduce0 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) otherwise",fontsize=16,color="black",shape="box"];1942 -> 2137[label="",style="solid", color="black", weight=3]; 1943 -> 207[label="",style="dashed", color="red", weight=0]; 1943[label="error []",fontsize=16,color="magenta"];2135[label="reduce2Reduce0 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) otherwise",fontsize=16,color="black",shape="box"];2135 -> 2155[label="",style="solid", color="black", weight=3]; 2136 -> 207[label="",style="dashed", color="red", weight=0]; 2136[label="error []",fontsize=16,color="magenta"];1015 -> 678[label="",style="dashed", color="red", weight=0]; 1015[label="primMulNat vuz310000 (Succ vuz4100)",fontsize=16,color="magenta"];1015 -> 1181[label="",style="dashed", color="magenta", weight=3]; 1925 -> 1352[label="",style="dashed", color="red", weight=0]; 1925[label="primPlusNat vuz6600 vuz41000",fontsize=16,color="magenta"];1925 -> 1946[label="",style="dashed", color="magenta", weight=3]; 1925 -> 1947[label="",style="dashed", color="magenta", weight=3]; 2204[label="reduce2Reduce0 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) True",fontsize=16,color="black",shape="box"];2204 -> 2220[label="",style="solid", color="black", weight=3]; 1536[label="reduce2Reduce0 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) True",fontsize=16,color="black",shape="box"];1536 -> 1719[label="",style="solid", color="black", weight=3]; 1714[label="reduce2Reduce0 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) True",fontsize=16,color="black",shape="box"];1714 -> 1898[label="",style="solid", color="black", weight=3]; 1897[label="reduce2Reduce0 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) True",fontsize=16,color="black",shape="box"];1897 -> 1926[label="",style="solid", color="black", weight=3]; 1924[label="reduce2Reduce0 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) True",fontsize=16,color="black",shape="box"];1924 -> 1945[label="",style="solid", color="black", weight=3]; 1944[label="reduce2Reduce0 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) True",fontsize=16,color="black",shape="box"];1944 -> 2138[label="",style="solid", color="black", weight=3]; 2137[label="reduce2Reduce0 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) True",fontsize=16,color="black",shape="box"];2137 -> 2156[label="",style="solid", color="black", weight=3]; 2155[label="reduce2Reduce0 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) True",fontsize=16,color="black",shape="box"];2155 -> 2170[label="",style="solid", color="black", weight=3]; 1181[label="vuz310000",fontsize=16,color="green",shape="box"];1946[label="vuz41000",fontsize=16,color="green",shape="box"];1947[label="vuz6600",fontsize=16,color="green",shape="box"];2220[label="(vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) `quot` reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) :% (Pos vuz143 `quot` reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144))",fontsize=16,color="green",shape="box"];2220 -> 2235[label="",style="dashed", color="green", weight=3]; 2220 -> 2236[label="",style="dashed", color="green", weight=3]; 1719[label="(vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) `quot` reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) :% (Neg vuz67 `quot` reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68))",fontsize=16,color="green",shape="box"];1719 -> 1899[label="",style="dashed", color="green", weight=3]; 1719 -> 1900[label="",style="dashed", color="green", weight=3]; 1898[label="(vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) `quot` reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) :% (Neg vuz70 `quot` reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71))",fontsize=16,color="green",shape="box"];1898 -> 1927[label="",style="dashed", color="green", weight=3]; 1898 -> 1928[label="",style="dashed", color="green", weight=3]; 1926[label="(vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) `quot` reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) :% (Pos vuz73 `quot` reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74))",fontsize=16,color="green",shape="box"];1926 -> 1948[label="",style="dashed", color="green", weight=3]; 1926 -> 1949[label="",style="dashed", color="green", weight=3]; 1945[label="(vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) `quot` reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) :% (Pos vuz76 `quot` reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77))",fontsize=16,color="green",shape="box"];1945 -> 2139[label="",style="dashed", color="green", weight=3]; 1945 -> 2140[label="",style="dashed", color="green", weight=3]; 2138[label="(vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) `quot` reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) :% (Neg vuz91 `quot` reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92))",fontsize=16,color="green",shape="box"];2138 -> 2157[label="",style="dashed", color="green", weight=3]; 2138 -> 2158[label="",style="dashed", color="green", weight=3]; 2156[label="(vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) `quot` reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) :% (Neg vuz106 `quot` reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107))",fontsize=16,color="green",shape="box"];2156 -> 2171[label="",style="dashed", color="green", weight=3]; 2156 -> 2172[label="",style="dashed", color="green", weight=3]; 2170[label="(vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) `quot` reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) :% (Pos vuz121 `quot` reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122))",fontsize=16,color="green",shape="box"];2170 -> 2187[label="",style="dashed", color="green", weight=3]; 2170 -> 2188[label="",style="dashed", color="green", weight=3]; 2235[label="(vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) `quot` reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];2235 -> 2248[label="",style="solid", color="black", weight=3]; 2236[label="Pos vuz143 `quot` reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];2236 -> 2249[label="",style="solid", color="black", weight=3]; 1899[label="(vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) `quot` reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];1899 -> 1929[label="",style="solid", color="black", weight=3]; 1900[label="Neg vuz67 `quot` reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];1900 -> 1930[label="",style="solid", color="black", weight=3]; 1927[label="(vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) `quot` reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];1927 -> 1950[label="",style="solid", color="black", weight=3]; 1928[label="Neg vuz70 `quot` reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];1928 -> 1951[label="",style="solid", color="black", weight=3]; 1948[label="(vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) `quot` reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];1948 -> 2141[label="",style="solid", color="black", weight=3]; 1949[label="Pos vuz73 `quot` reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];1949 -> 2142[label="",style="solid", color="black", weight=3]; 2139[label="(vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) `quot` reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];2139 -> 2159[label="",style="solid", color="black", weight=3]; 2140[label="Pos vuz76 `quot` reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];2140 -> 2160[label="",style="solid", color="black", weight=3]; 2157[label="(vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) `quot` reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];2157 -> 2173[label="",style="solid", color="black", weight=3]; 2158[label="Neg vuz91 `quot` reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];2158 -> 2174[label="",style="solid", color="black", weight=3]; 2171[label="(vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) `quot` reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];2171 -> 2189[label="",style="solid", color="black", weight=3]; 2172[label="Neg vuz106 `quot` reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];2172 -> 2190[label="",style="solid", color="black", weight=3]; 2187[label="(vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) `quot` reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];2187 -> 2205[label="",style="solid", color="black", weight=3]; 2188[label="Pos vuz121 `quot` reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];2188 -> 2206[label="",style="solid", color="black", weight=3]; 2248[label="primQuotInt (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144))",fontsize=16,color="black",shape="box"];2248 -> 2260[label="",style="solid", color="black", weight=3]; 2249 -> 5044[label="",style="dashed", color="red", weight=0]; 2249[label="primQuotInt (Pos vuz143) (reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144))",fontsize=16,color="magenta"];2249 -> 5045[label="",style="dashed", color="magenta", weight=3]; 2249 -> 5046[label="",style="dashed", color="magenta", weight=3]; 1929[label="primQuotInt (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68))",fontsize=16,color="black",shape="box"];1929 -> 1958[label="",style="solid", color="black", weight=3]; 1930 -> 3507[label="",style="dashed", color="red", weight=0]; 1930[label="primQuotInt (Neg vuz67) (reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68))",fontsize=16,color="magenta"];1930 -> 3508[label="",style="dashed", color="magenta", weight=3]; 1930 -> 3509[label="",style="dashed", color="magenta", weight=3]; 1950[label="primQuotInt (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71))",fontsize=16,color="black",shape="box"];1950 -> 2143[label="",style="solid", color="black", weight=3]; 1951 -> 3507[label="",style="dashed", color="red", weight=0]; 1951[label="primQuotInt (Neg vuz70) (reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71))",fontsize=16,color="magenta"];1951 -> 3510[label="",style="dashed", color="magenta", weight=3]; 1951 -> 3511[label="",style="dashed", color="magenta", weight=3]; 2141[label="primQuotInt (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74))",fontsize=16,color="black",shape="box"];2141 -> 2161[label="",style="solid", color="black", weight=3]; 2142 -> 5044[label="",style="dashed", color="red", weight=0]; 2142[label="primQuotInt (Pos vuz73) (reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74))",fontsize=16,color="magenta"];2142 -> 5047[label="",style="dashed", color="magenta", weight=3]; 2159[label="primQuotInt (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77))",fontsize=16,color="black",shape="box"];2159 -> 2175[label="",style="solid", color="black", weight=3]; 2160 -> 5044[label="",style="dashed", color="red", weight=0]; 2160[label="primQuotInt (Pos vuz76) (reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77))",fontsize=16,color="magenta"];2160 -> 5048[label="",style="dashed", color="magenta", weight=3]; 2160 -> 5049[label="",style="dashed", color="magenta", weight=3]; 2173[label="primQuotInt (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92))",fontsize=16,color="black",shape="box"];2173 -> 2191[label="",style="solid", color="black", weight=3]; 2174 -> 3507[label="",style="dashed", color="red", weight=0]; 2174[label="primQuotInt (Neg vuz91) (reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92))",fontsize=16,color="magenta"];2174 -> 3512[label="",style="dashed", color="magenta", weight=3]; 2174 -> 3513[label="",style="dashed", color="magenta", weight=3]; 2189[label="primQuotInt (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107))",fontsize=16,color="black",shape="box"];2189 -> 2207[label="",style="solid", color="black", weight=3]; 2190 -> 3507[label="",style="dashed", color="red", weight=0]; 2190[label="primQuotInt (Neg vuz106) (reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107))",fontsize=16,color="magenta"];2190 -> 3514[label="",style="dashed", color="magenta", weight=3]; 2190 -> 3515[label="",style="dashed", color="magenta", weight=3]; 2205[label="primQuotInt (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122))",fontsize=16,color="black",shape="box"];2205 -> 2221[label="",style="solid", color="black", weight=3]; 2206 -> 5044[label="",style="dashed", color="red", weight=0]; 2206[label="primQuotInt (Pos vuz121) (reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122))",fontsize=16,color="magenta"];2206 -> 5050[label="",style="dashed", color="magenta", weight=3]; 2206 -> 5051[label="",style="dashed", color="magenta", weight=3]; 2260[label="primQuotInt (primPlusInt (vuz9 * Pos (Succ vuz10)) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (vuz9 * Pos (Succ vuz10)) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2260 -> 2268[label="",style="solid", color="black", weight=3]; 5045[label="vuz143",fontsize=16,color="green",shape="box"];5046[label="reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5046 -> 5681[label="",style="solid", color="black", weight=3]; 5044[label="primQuotInt (Pos vuz73) vuz346",fontsize=16,color="burlywood",shape="triangle"];6472[label="vuz346/Pos vuz3460",fontsize=10,color="white",style="solid",shape="box"];5044 -> 6472[label="",style="solid", color="burlywood", weight=9]; 6472 -> 5682[label="",style="solid", color="burlywood", weight=3]; 6473[label="vuz346/Neg vuz3460",fontsize=10,color="white",style="solid",shape="box"];5044 -> 6473[label="",style="solid", color="burlywood", weight=9]; 6473 -> 5683[label="",style="solid", color="burlywood", weight=3]; 1958[label="primQuotInt (primPlusInt (vuz20 * Neg (Succ vuz21)) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (vuz20 * Neg (Succ vuz21)) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="box"];1958 -> 2145[label="",style="solid", color="black", weight=3]; 3508[label="reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];3508 -> 4082[label="",style="solid", color="black", weight=3]; 3509[label="vuz67",fontsize=16,color="green",shape="box"];3507[label="primQuotInt (Neg vuz280) vuz281",fontsize=16,color="burlywood",shape="triangle"];6474[label="vuz281/Pos vuz2810",fontsize=10,color="white",style="solid",shape="box"];3507 -> 6474[label="",style="solid", color="burlywood", weight=9]; 6474 -> 4083[label="",style="solid", color="burlywood", weight=3]; 6475[label="vuz281/Neg vuz2810",fontsize=10,color="white",style="solid",shape="box"];3507 -> 6475[label="",style="solid", color="burlywood", weight=9]; 6475 -> 4084[label="",style="solid", color="burlywood", weight=3]; 2143[label="primQuotInt (primPlusInt (vuz25 * Pos (Succ vuz26)) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (vuz25 * Pos (Succ vuz26)) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2143 -> 2163[label="",style="solid", color="black", weight=3]; 3510[label="reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];3510 -> 4085[label="",style="solid", color="black", weight=3]; 3511[label="vuz70",fontsize=16,color="green",shape="box"];2161[label="primQuotInt (primPlusInt (vuz30 * Neg (Succ vuz31)) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (vuz30 * Neg (Succ vuz31)) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2161 -> 2177[label="",style="solid", color="black", weight=3]; 5047[label="reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5047 -> 5684[label="",style="solid", color="black", weight=3]; 2175[label="primQuotInt (primPlusInt (vuz35 * Pos (Succ vuz36)) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (vuz35 * Pos (Succ vuz36)) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2175 -> 2193[label="",style="solid", color="black", weight=3]; 5048[label="vuz76",fontsize=16,color="green",shape="box"];5049[label="reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5049 -> 5685[label="",style="solid", color="black", weight=3]; 2191[label="primQuotInt (primPlusInt (vuz40 * Neg (Succ vuz41)) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (vuz40 * Neg (Succ vuz41)) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2191 -> 2209[label="",style="solid", color="black", weight=3]; 3512[label="reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];3512 -> 4086[label="",style="solid", color="black", weight=3]; 3513[label="vuz91",fontsize=16,color="green",shape="box"];2207[label="primQuotInt (primPlusInt (vuz45 * Pos (Succ vuz46)) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (vuz45 * Pos (Succ vuz46)) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2207 -> 2223[label="",style="solid", color="black", weight=3]; 3514[label="reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];3514 -> 4087[label="",style="solid", color="black", weight=3]; 3515[label="vuz106",fontsize=16,color="green",shape="box"];2221[label="primQuotInt (primPlusInt (vuz50 * Neg (Succ vuz51)) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (vuz50 * Neg (Succ vuz51)) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2221 -> 2237[label="",style="solid", color="black", weight=3]; 5050[label="vuz121",fontsize=16,color="green",shape="box"];5051[label="reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5051 -> 5686[label="",style="solid", color="black", weight=3]; 2268[label="primQuotInt (primPlusInt (primMulInt vuz9 (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (primMulInt vuz9 (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="burlywood",shape="box"];6476[label="vuz9/Pos vuz90",fontsize=10,color="white",style="solid",shape="box"];2268 -> 6476[label="",style="solid", color="burlywood", weight=9]; 6476 -> 2274[label="",style="solid", color="burlywood", weight=3]; 6477[label="vuz9/Neg vuz90",fontsize=10,color="white",style="solid",shape="box"];2268 -> 6477[label="",style="solid", color="burlywood", weight=9]; 6477 -> 2275[label="",style="solid", color="burlywood", weight=3]; 5681[label="gcd (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5681 -> 5695[label="",style="solid", color="black", weight=3]; 5682[label="primQuotInt (Pos vuz73) (Pos vuz3460)",fontsize=16,color="burlywood",shape="box"];6478[label="vuz3460/Succ vuz34600",fontsize=10,color="white",style="solid",shape="box"];5682 -> 6478[label="",style="solid", color="burlywood", weight=9]; 6478 -> 5696[label="",style="solid", color="burlywood", weight=3]; 6479[label="vuz3460/Zero",fontsize=10,color="white",style="solid",shape="box"];5682 -> 6479[label="",style="solid", color="burlywood", weight=9]; 6479 -> 5697[label="",style="solid", color="burlywood", weight=3]; 5683[label="primQuotInt (Pos vuz73) (Neg vuz3460)",fontsize=16,color="burlywood",shape="box"];6480[label="vuz3460/Succ vuz34600",fontsize=10,color="white",style="solid",shape="box"];5683 -> 6480[label="",style="solid", color="burlywood", weight=9]; 6480 -> 5698[label="",style="solid", color="burlywood", weight=3]; 6481[label="vuz3460/Zero",fontsize=10,color="white",style="solid",shape="box"];5683 -> 6481[label="",style="solid", color="burlywood", weight=9]; 6481 -> 5699[label="",style="solid", color="burlywood", weight=3]; 2145[label="primQuotInt (primPlusInt (primMulInt vuz20 (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (primMulInt vuz20 (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="burlywood",shape="box"];6482[label="vuz20/Pos vuz200",fontsize=10,color="white",style="solid",shape="box"];2145 -> 6482[label="",style="solid", color="burlywood", weight=9]; 6482 -> 2165[label="",style="solid", color="burlywood", weight=3]; 6483[label="vuz20/Neg vuz200",fontsize=10,color="white",style="solid",shape="box"];2145 -> 6483[label="",style="solid", color="burlywood", weight=9]; 6483 -> 2166[label="",style="solid", color="burlywood", weight=3]; 4082[label="gcd (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4082 -> 4091[label="",style="solid", color="black", weight=3]; 4083[label="primQuotInt (Neg vuz280) (Pos vuz2810)",fontsize=16,color="burlywood",shape="box"];6484[label="vuz2810/Succ vuz28100",fontsize=10,color="white",style="solid",shape="box"];4083 -> 6484[label="",style="solid", color="burlywood", weight=9]; 6484 -> 4092[label="",style="solid", color="burlywood", weight=3]; 6485[label="vuz2810/Zero",fontsize=10,color="white",style="solid",shape="box"];4083 -> 6485[label="",style="solid", color="burlywood", weight=9]; 6485 -> 4093[label="",style="solid", color="burlywood", weight=3]; 4084[label="primQuotInt (Neg vuz280) (Neg vuz2810)",fontsize=16,color="burlywood",shape="box"];6486[label="vuz2810/Succ vuz28100",fontsize=10,color="white",style="solid",shape="box"];4084 -> 6486[label="",style="solid", color="burlywood", weight=9]; 6486 -> 4094[label="",style="solid", color="burlywood", weight=3]; 6487[label="vuz2810/Zero",fontsize=10,color="white",style="solid",shape="box"];4084 -> 6487[label="",style="solid", color="burlywood", weight=9]; 6487 -> 4095[label="",style="solid", color="burlywood", weight=3]; 2163[label="primQuotInt (primPlusInt (primMulInt vuz25 (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (primMulInt vuz25 (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="burlywood",shape="box"];6488[label="vuz25/Pos vuz250",fontsize=10,color="white",style="solid",shape="box"];2163 -> 6488[label="",style="solid", color="burlywood", weight=9]; 6488 -> 2179[label="",style="solid", color="burlywood", weight=3]; 6489[label="vuz25/Neg vuz250",fontsize=10,color="white",style="solid",shape="box"];2163 -> 6489[label="",style="solid", color="burlywood", weight=9]; 6489 -> 2180[label="",style="solid", color="burlywood", weight=3]; 4085[label="gcd (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];4085 -> 4096[label="",style="solid", color="black", weight=3]; 2177[label="primQuotInt (primPlusInt (primMulInt vuz30 (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (primMulInt vuz30 (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="burlywood",shape="box"];6490[label="vuz30/Pos vuz300",fontsize=10,color="white",style="solid",shape="box"];2177 -> 6490[label="",style="solid", color="burlywood", weight=9]; 6490 -> 2195[label="",style="solid", color="burlywood", weight=3]; 6491[label="vuz30/Neg vuz300",fontsize=10,color="white",style="solid",shape="box"];2177 -> 6491[label="",style="solid", color="burlywood", weight=9]; 6491 -> 2196[label="",style="solid", color="burlywood", weight=3]; 5684[label="gcd (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5684 -> 5700[label="",style="solid", color="black", weight=3]; 2193[label="primQuotInt (primPlusInt (primMulInt vuz35 (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (primMulInt vuz35 (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="burlywood",shape="box"];6492[label="vuz35/Pos vuz350",fontsize=10,color="white",style="solid",shape="box"];2193 -> 6492[label="",style="solid", color="burlywood", weight=9]; 6492 -> 2211[label="",style="solid", color="burlywood", weight=3]; 6493[label="vuz35/Neg vuz350",fontsize=10,color="white",style="solid",shape="box"];2193 -> 6493[label="",style="solid", color="burlywood", weight=9]; 6493 -> 2212[label="",style="solid", color="burlywood", weight=3]; 5685[label="gcd (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5685 -> 5701[label="",style="solid", color="black", weight=3]; 2209[label="primQuotInt (primPlusInt (primMulInt vuz40 (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (primMulInt vuz40 (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="burlywood",shape="box"];6494[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];2209 -> 6494[label="",style="solid", color="burlywood", weight=9]; 6494 -> 2225[label="",style="solid", color="burlywood", weight=3]; 6495[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];2209 -> 6495[label="",style="solid", color="burlywood", weight=9]; 6495 -> 2226[label="",style="solid", color="burlywood", weight=3]; 4086[label="gcd (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];4086 -> 4097[label="",style="solid", color="black", weight=3]; 2223[label="primQuotInt (primPlusInt (primMulInt vuz45 (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (primMulInt vuz45 (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="burlywood",shape="box"];6496[label="vuz45/Pos vuz450",fontsize=10,color="white",style="solid",shape="box"];2223 -> 6496[label="",style="solid", color="burlywood", weight=9]; 6496 -> 2239[label="",style="solid", color="burlywood", weight=3]; 6497[label="vuz45/Neg vuz450",fontsize=10,color="white",style="solid",shape="box"];2223 -> 6497[label="",style="solid", color="burlywood", weight=9]; 6497 -> 2240[label="",style="solid", color="burlywood", weight=3]; 4087[label="gcd (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];4087 -> 4098[label="",style="solid", color="black", weight=3]; 2237[label="primQuotInt (primPlusInt (primMulInt vuz50 (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (primMulInt vuz50 (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="burlywood",shape="box"];6498[label="vuz50/Pos vuz500",fontsize=10,color="white",style="solid",shape="box"];2237 -> 6498[label="",style="solid", color="burlywood", weight=9]; 6498 -> 2250[label="",style="solid", color="burlywood", weight=3]; 6499[label="vuz50/Neg vuz500",fontsize=10,color="white",style="solid",shape="box"];2237 -> 6499[label="",style="solid", color="burlywood", weight=9]; 6499 -> 2251[label="",style="solid", color="burlywood", weight=3]; 5686[label="gcd (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5686 -> 5702[label="",style="solid", color="black", weight=3]; 2274[label="primQuotInt (primPlusInt (primMulInt (Pos vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (primMulInt (Pos vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2274 -> 2280[label="",style="solid", color="black", weight=3]; 2275[label="primQuotInt (primPlusInt (primMulInt (Neg vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (primMulInt (Neg vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2275 -> 2281[label="",style="solid", color="black", weight=3]; 5695[label="gcd3 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5695 -> 5711[label="",style="solid", color="black", weight=3]; 5696[label="primQuotInt (Pos vuz73) (Pos (Succ vuz34600))",fontsize=16,color="black",shape="box"];5696 -> 5712[label="",style="solid", color="black", weight=3]; 5697[label="primQuotInt (Pos vuz73) (Pos Zero)",fontsize=16,color="black",shape="box"];5697 -> 5713[label="",style="solid", color="black", weight=3]; 5698[label="primQuotInt (Pos vuz73) (Neg (Succ vuz34600))",fontsize=16,color="black",shape="box"];5698 -> 5714[label="",style="solid", color="black", weight=3]; 5699[label="primQuotInt (Pos vuz73) (Neg Zero)",fontsize=16,color="black",shape="box"];5699 -> 5715[label="",style="solid", color="black", weight=3]; 2165[label="primQuotInt (primPlusInt (primMulInt (Pos vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (primMulInt (Pos vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="box"];2165 -> 2182[label="",style="solid", color="black", weight=3]; 2166[label="primQuotInt (primPlusInt (primMulInt (Neg vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (primMulInt (Neg vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="box"];2166 -> 2183[label="",style="solid", color="black", weight=3]; 4091[label="gcd3 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4091 -> 4104[label="",style="solid", color="black", weight=3]; 4092[label="primQuotInt (Neg vuz280) (Pos (Succ vuz28100))",fontsize=16,color="black",shape="box"];4092 -> 4105[label="",style="solid", color="black", weight=3]; 4093[label="primQuotInt (Neg vuz280) (Pos Zero)",fontsize=16,color="black",shape="box"];4093 -> 4106[label="",style="solid", color="black", weight=3]; 4094[label="primQuotInt (Neg vuz280) (Neg (Succ vuz28100))",fontsize=16,color="black",shape="box"];4094 -> 4107[label="",style="solid", color="black", weight=3]; 4095[label="primQuotInt (Neg vuz280) (Neg Zero)",fontsize=16,color="black",shape="box"];4095 -> 4108[label="",style="solid", color="black", weight=3]; 2179[label="primQuotInt (primPlusInt (primMulInt (Pos vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (primMulInt (Pos vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2179 -> 2198[label="",style="solid", color="black", weight=3]; 2180[label="primQuotInt (primPlusInt (primMulInt (Neg vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (primMulInt (Neg vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2180 -> 2199[label="",style="solid", color="black", weight=3]; 4096[label="gcd3 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];4096 -> 4109[label="",style="solid", color="black", weight=3]; 2195[label="primQuotInt (primPlusInt (primMulInt (Pos vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (primMulInt (Pos vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2195 -> 2214[label="",style="solid", color="black", weight=3]; 2196[label="primQuotInt (primPlusInt (primMulInt (Neg vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (primMulInt (Neg vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2196 -> 2215[label="",style="solid", color="black", weight=3]; 5700[label="gcd3 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5700 -> 5716[label="",style="solid", color="black", weight=3]; 2211[label="primQuotInt (primPlusInt (primMulInt (Pos vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (primMulInt (Pos vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2211 -> 2228[label="",style="solid", color="black", weight=3]; 2212[label="primQuotInt (primPlusInt (primMulInt (Neg vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (primMulInt (Neg vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2212 -> 2229[label="",style="solid", color="black", weight=3]; 5701[label="gcd3 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5701 -> 5717[label="",style="solid", color="black", weight=3]; 2225[label="primQuotInt (primPlusInt (primMulInt (Pos vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (primMulInt (Pos vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2225 -> 2242[label="",style="solid", color="black", weight=3]; 2226[label="primQuotInt (primPlusInt (primMulInt (Neg vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (primMulInt (Neg vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2226 -> 2243[label="",style="solid", color="black", weight=3]; 4097[label="gcd3 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];4097 -> 4110[label="",style="solid", color="black", weight=3]; 2239[label="primQuotInt (primPlusInt (primMulInt (Pos vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (primMulInt (Pos vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2239 -> 2253[label="",style="solid", color="black", weight=3]; 2240[label="primQuotInt (primPlusInt (primMulInt (Neg vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (primMulInt (Neg vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2240 -> 2254[label="",style="solid", color="black", weight=3]; 4098[label="gcd3 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];4098 -> 4111[label="",style="solid", color="black", weight=3]; 2250[label="primQuotInt (primPlusInt (primMulInt (Pos vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (primMulInt (Pos vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2250 -> 2262[label="",style="solid", color="black", weight=3]; 2251[label="primQuotInt (primPlusInt (primMulInt (Neg vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (primMulInt (Neg vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2251 -> 2263[label="",style="solid", color="black", weight=3]; 5702[label="gcd3 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5702 -> 5718[label="",style="solid", color="black", weight=3]; 2280 -> 2287[label="",style="dashed", color="red", weight=0]; 2280[label="primQuotInt (primPlusInt (Pos (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (Pos (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="magenta"];2280 -> 2288[label="",style="dashed", color="magenta", weight=3]; 2280 -> 2289[label="",style="dashed", color="magenta", weight=3]; 2281 -> 2290[label="",style="dashed", color="red", weight=0]; 2281[label="primQuotInt (primPlusInt (Neg (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (Neg (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="magenta"];2281 -> 2291[label="",style="dashed", color="magenta", weight=3]; 2281 -> 2292[label="",style="dashed", color="magenta", weight=3]; 5711[label="gcd2 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12) == fromInt (Pos Zero)) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5711 -> 5733[label="",style="solid", color="black", weight=3]; 5712[label="Pos (primDivNatS vuz73 (Succ vuz34600))",fontsize=16,color="green",shape="box"];5712 -> 5734[label="",style="dashed", color="green", weight=3]; 5713 -> 4106[label="",style="dashed", color="red", weight=0]; 5713[label="error []",fontsize=16,color="magenta"];5714[label="Neg (primDivNatS vuz73 (Succ vuz34600))",fontsize=16,color="green",shape="box"];5714 -> 5735[label="",style="dashed", color="green", weight=3]; 5715 -> 4106[label="",style="dashed", color="red", weight=0]; 5715[label="error []",fontsize=16,color="magenta"];2182 -> 2201[label="",style="dashed", color="red", weight=0]; 2182[label="primQuotInt (primPlusInt (Neg (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (Neg (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="magenta"];2182 -> 2202[label="",style="dashed", color="magenta", weight=3]; 2182 -> 2203[label="",style="dashed", color="magenta", weight=3]; 2183 -> 2217[label="",style="dashed", color="red", weight=0]; 2183[label="primQuotInt (primPlusInt (Pos (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (Pos (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="magenta"];2183 -> 2218[label="",style="dashed", color="magenta", weight=3]; 2183 -> 2219[label="",style="dashed", color="magenta", weight=3]; 4104[label="gcd2 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23) == fromInt (Pos Zero)) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4104 -> 4126[label="",style="solid", color="black", weight=3]; 4105[label="Neg (primDivNatS vuz280 (Succ vuz28100))",fontsize=16,color="green",shape="box"];4105 -> 4127[label="",style="dashed", color="green", weight=3]; 4106[label="error []",fontsize=16,color="black",shape="triangle"];4106 -> 4128[label="",style="solid", color="black", weight=3]; 4107[label="Pos (primDivNatS vuz280 (Succ vuz28100))",fontsize=16,color="green",shape="box"];4107 -> 4129[label="",style="dashed", color="green", weight=3]; 4108 -> 4106[label="",style="dashed", color="red", weight=0]; 4108[label="error []",fontsize=16,color="magenta"];2198 -> 2232[label="",style="dashed", color="red", weight=0]; 2198[label="primQuotInt (primPlusInt (Pos (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (Pos (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="magenta"];2198 -> 2233[label="",style="dashed", color="magenta", weight=3]; 2198 -> 2234[label="",style="dashed", color="magenta", weight=3]; 2199 -> 2245[label="",style="dashed", color="red", weight=0]; 2199[label="primQuotInt (primPlusInt (Neg (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (Neg (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="magenta"];2199 -> 2246[label="",style="dashed", color="magenta", weight=3]; 2199 -> 2247[label="",style="dashed", color="magenta", weight=3]; 4109[label="gcd2 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28) == fromInt (Pos Zero)) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];4109 -> 4130[label="",style="solid", color="black", weight=3]; 2214 -> 2257[label="",style="dashed", color="red", weight=0]; 2214[label="primQuotInt (primPlusInt (Neg (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (Neg (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="magenta"];2214 -> 2258[label="",style="dashed", color="magenta", weight=3]; 2214 -> 2259[label="",style="dashed", color="magenta", weight=3]; 2215 -> 2265[label="",style="dashed", color="red", weight=0]; 2215[label="primQuotInt (primPlusInt (Pos (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (Pos (primMulNat vuz300 (Succ vuz31))) 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2229[label="primQuotInt (primPlusInt (Neg (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (Neg (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="magenta"];2229 -> 2278[label="",style="dashed", color="magenta", weight=3]; 2229 -> 2279[label="",style="dashed", color="magenta", weight=3]; 5717[label="gcd2 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38) == fromInt (Pos Zero)) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5717 -> 5737[label="",style="solid", color="black", weight=3]; 2242 -> 2284[label="",style="dashed", color="red", weight=0]; 2242[label="primQuotInt (primPlusInt (Neg (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (Neg (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="magenta"];2242 -> 2285[label="",style="dashed", 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color="red", weight=0]; 2262[label="primQuotInt (primPlusInt (Neg (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (Neg (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="magenta"];2262 -> 2306[label="",style="dashed", color="magenta", weight=3]; 2262 -> 2307[label="",style="dashed", color="magenta", weight=3]; 2263 -> 2308[label="",style="dashed", color="red", weight=0]; 2263[label="primQuotInt (primPlusInt (Pos (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (Pos (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="magenta"];2263 -> 2309[label="",style="dashed", color="magenta", weight=3]; 2263 -> 2310[label="",style="dashed", color="magenta", weight=3]; 5718[label="gcd2 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53) == fromInt (Pos Zero)) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5718 -> 5738[label="",style="solid", color="black", weight=3]; 2288 -> 678[label="",style="dashed", color="red", weight=0]; 2288[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];2288 -> 2312[label="",style="dashed", color="magenta", weight=3]; 2288 -> 2313[label="",style="dashed", color="magenta", weight=3]; 2289 -> 678[label="",style="dashed", color="red", weight=0]; 2289[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];2289 -> 2314[label="",style="dashed", color="magenta", weight=3]; 2289 -> 2315[label="",style="dashed", color="magenta", weight=3]; 2287[label="primQuotInt (primPlusInt (Pos vuz185) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (Pos vuz186) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="triangle"];2287 -> 2316[label="",style="solid", color="black", weight=3]; 2291 -> 678[label="",style="dashed", color="red", weight=0]; 2291[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];2291 -> 2317[label="",style="dashed", color="magenta", weight=3]; 2291 -> 2318[label="",style="dashed", color="magenta", weight=3]; 2292 -> 678[label="",style="dashed", color="red", weight=0]; 2292[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];2292 -> 2319[label="",style="dashed", color="magenta", weight=3]; 2292 -> 2320[label="",style="dashed", color="magenta", weight=3]; 2290[label="primQuotInt (primPlusInt (Neg vuz187) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (Neg vuz188) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="triangle"];2290 -> 2321[label="",style="solid", color="black", weight=3]; 5733[label="gcd2 (primEqInt (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (fromInt (Pos Zero))) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5733 -> 5748[label="",style="solid", color="black", weight=3]; 5734 -> 4127[label="",style="dashed", color="red", weight=0]; 5734[label="primDivNatS vuz73 (Succ vuz34600)",fontsize=16,color="magenta"];5734 -> 5749[label="",style="dashed", color="magenta", weight=3]; 5734 -> 5750[label="",style="dashed", color="magenta", weight=3]; 5735 -> 4127[label="",style="dashed", color="red", weight=0]; 5735[label="primDivNatS vuz73 (Succ vuz34600)",fontsize=16,color="magenta"];5735 -> 5751[label="",style="dashed", color="magenta", weight=3]; 5735 -> 5752[label="",style="dashed", color="magenta", weight=3]; 2202 -> 678[label="",style="dashed", color="red", weight=0]; 2202[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];2202 -> 2323[label="",style="dashed", color="magenta", weight=3]; 2202 -> 2324[label="",style="dashed", color="magenta", weight=3]; 2203 -> 678[label="",style="dashed", color="red", weight=0]; 2203[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];2203 -> 2325[label="",style="dashed", color="magenta", weight=3]; 2203 -> 2326[label="",style="dashed", color="magenta", weight=3]; 2201[label="primQuotInt (primPlusInt (Neg vuz167) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (Neg vuz168) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="triangle"];2201 -> 2327[label="",style="solid", color="black", weight=3]; 2218 -> 678[label="",style="dashed", color="red", weight=0]; 2218[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];2218 -> 2328[label="",style="dashed", color="magenta", weight=3]; 2218 -> 2329[label="",style="dashed", color="magenta", weight=3]; 2219 -> 678[label="",style="dashed", color="red", weight=0]; 2219[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];2219 -> 2330[label="",style="dashed", color="magenta", weight=3]; 2219 -> 2331[label="",style="dashed", color="magenta", weight=3]; 2217[label="primQuotInt (primPlusInt (Pos vuz169) (Neg vuz22 * Pos (Succ 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weight=3]; 4128[label="error []",fontsize=16,color="red",shape="box"];4129 -> 4127[label="",style="dashed", color="red", weight=0]; 4129[label="primDivNatS vuz280 (Succ vuz28100)",fontsize=16,color="magenta"];4129 -> 4145[label="",style="dashed", color="magenta", weight=3]; 2233 -> 678[label="",style="dashed", color="red", weight=0]; 2233[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];2233 -> 2334[label="",style="dashed", color="magenta", weight=3]; 2233 -> 2335[label="",style="dashed", color="magenta", weight=3]; 2234 -> 678[label="",style="dashed", color="red", weight=0]; 2234[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];2234 -> 2336[label="",style="dashed", color="magenta", weight=3]; 2234 -> 2337[label="",style="dashed", color="magenta", weight=3]; 2232[label="primQuotInt (primPlusInt (Pos vuz171) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (Pos vuz172) (Neg vuz27 * Neg (Succ vuz28))) (Neg 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weight=3]; 2266 -> 678[label="",style="dashed", color="red", weight=0]; 2266[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];2266 -> 2350[label="",style="dashed", color="magenta", weight=3]; 2266 -> 2351[label="",style="dashed", color="magenta", weight=3]; 2267 -> 678[label="",style="dashed", color="red", weight=0]; 2267[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];2267 -> 2352[label="",style="dashed", color="magenta", weight=3]; 2267 -> 2353[label="",style="dashed", color="magenta", weight=3]; 2265[label="primQuotInt (primPlusInt (Pos vuz177) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (Pos vuz178) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="triangle"];2265 -> 2354[label="",style="solid", color="black", weight=3]; 5736[label="gcd2 (primEqInt (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (fromInt (Pos Zero))) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5736 -> 5753[label="",style="solid", color="black", weight=3]; 2272 -> 678[label="",style="dashed", color="red", weight=0]; 2272[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];2272 -> 2356[label="",style="dashed", color="magenta", weight=3]; 2272 -> 2357[label="",style="dashed", color="magenta", weight=3]; 2273 -> 678[label="",style="dashed", color="red", weight=0]; 2273[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];2273 -> 2358[label="",style="dashed", color="magenta", weight=3]; 2273 -> 2359[label="",style="dashed", color="magenta", weight=3]; 2271[label="primQuotInt (primPlusInt (Pos vuz179) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (Pos vuz180) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="triangle"];2271 -> 2360[label="",style="solid", color="black", weight=3]; 2278 -> 678[label="",style="dashed", color="red", weight=0]; 2278[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];2278 -> 2361[label="",style="dashed", color="magenta", weight=3]; 2278 -> 2362[label="",style="dashed", color="magenta", weight=3]; 2279 -> 678[label="",style="dashed", color="red", weight=0]; 2279[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];2279 -> 2363[label="",style="dashed", color="magenta", weight=3]; 2279 -> 2364[label="",style="dashed", color="magenta", weight=3]; 2277[label="primQuotInt (primPlusInt (Neg vuz181) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (Neg vuz182) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="triangle"];2277 -> 2365[label="",style="solid", color="black", weight=3]; 5737[label="gcd2 (primEqInt (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (fromInt (Pos Zero))) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5737 -> 5754[label="",style="solid", color="black", weight=3]; 2285 -> 678[label="",style="dashed", color="red", weight=0]; 2285[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];2285 -> 2367[label="",style="dashed", color="magenta", weight=3]; 2285 -> 2368[label="",style="dashed", color="magenta", weight=3]; 2286 -> 678[label="",style="dashed", color="red", weight=0]; 2286[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];2286 -> 2369[label="",style="dashed", color="magenta", weight=3]; 2286 -> 2370[label="",style="dashed", color="magenta", weight=3]; 2284[label="primQuotInt (primPlusInt (Neg vuz183) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (Neg vuz184) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="triangle"];2284 -> 2371[label="",style="solid", color="black", weight=3]; 2295 -> 678[label="",style="dashed", color="red", weight=0]; 2295[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];2295 -> 2372[label="",style="dashed", color="magenta", weight=3]; 2295 -> 2373[label="",style="dashed", color="magenta", weight=3]; 2296 -> 678[label="",style="dashed", color="red", weight=0]; 2296[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];2296 -> 2374[label="",style="dashed", color="magenta", weight=3]; 2296 -> 2375[label="",style="dashed", color="magenta", weight=3]; 2294[label="primQuotInt (primPlusInt (Pos vuz189) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (Pos vuz190) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="triangle"];2294 -> 2376[label="",style="solid", color="black", weight=3]; 4131[label="gcd2 (primEqInt (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (fromInt (Pos Zero))) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];4131 -> 4147[label="",style="solid", color="black", weight=3]; 2299 -> 678[label="",style="dashed", color="red", weight=0]; 2299[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];2299 -> 2378[label="",style="dashed", color="magenta", weight=3]; 2299 -> 2379[label="",style="dashed", color="magenta", weight=3]; 2300 -> 678[label="",style="dashed", color="red", weight=0]; 2300[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];2300 -> 2380[label="",style="dashed", color="magenta", weight=3]; 2300 -> 2381[label="",style="dashed", color="magenta", weight=3]; 2298[label="primQuotInt (primPlusInt (Pos vuz191) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (Pos vuz192) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="triangle"];2298 -> 2382[label="",style="solid", color="black", weight=3]; 2302 -> 678[label="",style="dashed", color="red", weight=0]; 2302[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];2302 -> 2383[label="",style="dashed", color="magenta", weight=3]; 2302 -> 2384[label="",style="dashed", color="magenta", weight=3]; 2303 -> 678[label="",style="dashed", color="red", weight=0]; 2303[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];2303 -> 2385[label="",style="dashed", color="magenta", weight=3]; 2303 -> 2386[label="",style="dashed", color="magenta", weight=3]; 2301[label="primQuotInt (primPlusInt (Neg vuz193) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (Neg vuz194) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="triangle"];2301 -> 2387[label="",style="solid", color="black", weight=3]; 4132[label="gcd2 (primEqInt (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (fromInt (Pos Zero))) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];4132 -> 4148[label="",style="solid", color="black", weight=3]; 2306 -> 678[label="",style="dashed", color="red", weight=0]; 2306[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];2306 -> 2389[label="",style="dashed", color="magenta", weight=3]; 2306 -> 2390[label="",style="dashed", color="magenta", weight=3]; 2307 -> 678[label="",style="dashed", color="red", weight=0]; 2307[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];2307 -> 2391[label="",style="dashed", color="magenta", weight=3]; 2307 -> 2392[label="",style="dashed", color="magenta", weight=3]; 2305[label="primQuotInt (primPlusInt (Neg vuz195) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (Neg vuz196) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="triangle"];2305 -> 2393[label="",style="solid", color="black", weight=3]; 2309 -> 678[label="",style="dashed", color="red", weight=0]; 2309[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];2309 -> 2394[label="",style="dashed", color="magenta", weight=3]; 2309 -> 2395[label="",style="dashed", color="magenta", weight=3]; 2310 -> 678[label="",style="dashed", color="red", weight=0]; 2310[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];2310 -> 2396[label="",style="dashed", color="magenta", weight=3]; 2310 -> 2397[label="",style="dashed", color="magenta", weight=3]; 2308[label="primQuotInt (primPlusInt (Pos vuz197) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (Pos vuz198) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="triangle"];2308 -> 2398[label="",style="solid", color="black", weight=3]; 5738[label="gcd2 (primEqInt (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (fromInt (Pos Zero))) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5738 -> 5755[label="",style="solid", color="black", weight=3]; 2312[label="vuz90",fontsize=16,color="green",shape="box"];2313[label="vuz10",fontsize=16,color="green",shape="box"];2314[label="vuz90",fontsize=16,color="green",shape="box"];2315[label="vuz10",fontsize=16,color="green",shape="box"];2316[label="primQuotInt (primPlusInt (Pos vuz185) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (reduce2D (primPlusInt (Pos vuz186) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2316 -> 2400[label="",style="solid", color="black", weight=3]; 2317[label="vuz90",fontsize=16,color="green",shape="box"];2318[label="vuz10",fontsize=16,color="green",shape="box"];2319[label="vuz90",fontsize=16,color="green",shape="box"];2320[label="vuz10",fontsize=16,color="green",shape="box"];2321[label="primQuotInt (primPlusInt (Neg vuz187) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (reduce2D (primPlusInt (Neg vuz188) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2321 -> 2401[label="",style="solid", color="black", weight=3]; 5748[label="gcd2 (primEqInt (primPlusInt (vuz9 * Pos (Succ vuz10)) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (vuz9 * Pos (Succ vuz10)) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5748 -> 5767[label="",style="solid", color="black", weight=3]; 5749[label="vuz34600",fontsize=16,color="green",shape="box"];5750[label="vuz73",fontsize=16,color="green",shape="box"];5751[label="vuz34600",fontsize=16,color="green",shape="box"];5752[label="vuz73",fontsize=16,color="green",shape="box"];2323[label="vuz200",fontsize=16,color="green",shape="box"];2324[label="vuz21",fontsize=16,color="green",shape="box"];2325[label="vuz200",fontsize=16,color="green",shape="box"];2326[label="vuz21",fontsize=16,color="green",shape="box"];2327[label="primQuotInt (primPlusInt (Neg vuz167) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (reduce2D (primPlusInt (Neg vuz168) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (Neg vuz68))",fontsize=16,color="black",shape="box"];2327 -> 2404[label="",style="solid", color="black", weight=3]; 2328[label="vuz200",fontsize=16,color="green",shape="box"];2329[label="vuz21",fontsize=16,color="green",shape="box"];2330[label="vuz200",fontsize=16,color="green",shape="box"];2331[label="vuz21",fontsize=16,color="green",shape="box"];2332[label="primQuotInt (primPlusInt (Pos vuz169) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (reduce2D (primPlusInt (Pos vuz170) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (Neg vuz68))",fontsize=16,color="black",shape="box"];2332 -> 2405[label="",style="solid", color="black", weight=3]; 4142[label="gcd2 (primEqInt (primPlusInt (vuz20 * Neg (Succ vuz21)) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (vuz20 * Neg (Succ vuz21)) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4142 -> 4158[label="",style="solid", color="black", weight=3]; 4143[label="primDivNatS (Succ vuz2800) (Succ vuz28100)",fontsize=16,color="black",shape="box"];4143 -> 4159[label="",style="solid", color="black", weight=3]; 4144[label="primDivNatS Zero (Succ vuz28100)",fontsize=16,color="black",shape="box"];4144 -> 4160[label="",style="solid", color="black", weight=3]; 4145[label="vuz28100",fontsize=16,color="green",shape="box"];2334[label="vuz250",fontsize=16,color="green",shape="box"];2335[label="vuz26",fontsize=16,color="green",shape="box"];2336[label="vuz250",fontsize=16,color="green",shape="box"];2337[label="vuz26",fontsize=16,color="green",shape="box"];2338[label="primQuotInt (primPlusInt (Pos vuz171) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (reduce2D (primPlusInt (Pos vuz172) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2338 -> 2408[label="",style="solid", color="black", weight=3]; 2339[label="vuz250",fontsize=16,color="green",shape="box"];2340[label="vuz26",fontsize=16,color="green",shape="box"];2341[label="vuz250",fontsize=16,color="green",shape="box"];2342[label="vuz26",fontsize=16,color="green",shape="box"];2343[label="primQuotInt (primPlusInt (Neg vuz173) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (reduce2D (primPlusInt (Neg vuz174) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2343 -> 2409[label="",style="solid", color="black", weight=3]; 4146[label="gcd2 (primEqInt (primPlusInt (vuz25 * Pos (Succ vuz26)) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (vuz25 * Pos (Succ vuz26)) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4146 -> 4161[label="",style="solid", color="black", weight=3]; 2345[label="vuz300",fontsize=16,color="green",shape="box"];2346[label="vuz31",fontsize=16,color="green",shape="box"];2347[label="vuz300",fontsize=16,color="green",shape="box"];2348[label="vuz31",fontsize=16,color="green",shape="box"];2349[label="primQuotInt (primPlusInt (Neg vuz175) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (reduce2D (primPlusInt (Neg vuz176) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2349 -> 2412[label="",style="solid", color="black", weight=3]; 2350[label="vuz300",fontsize=16,color="green",shape="box"];2351[label="vuz31",fontsize=16,color="green",shape="box"];2352[label="vuz300",fontsize=16,color="green",shape="box"];2353[label="vuz31",fontsize=16,color="green",shape="box"];2354[label="primQuotInt (primPlusInt (Pos vuz177) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (reduce2D (primPlusInt (Pos vuz178) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2354 -> 2413[label="",style="solid", color="black", weight=3]; 5753[label="gcd2 (primEqInt (primPlusInt (vuz30 * Neg (Succ vuz31)) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (vuz30 * Neg (Succ vuz31)) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5753 -> 5768[label="",style="solid", color="black", weight=3]; 2356[label="vuz350",fontsize=16,color="green",shape="box"];2357[label="vuz36",fontsize=16,color="green",shape="box"];2358[label="vuz350",fontsize=16,color="green",shape="box"];2359[label="vuz36",fontsize=16,color="green",shape="box"];2360[label="primQuotInt (primPlusInt (Pos vuz179) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (reduce2D (primPlusInt (Pos vuz180) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2360 -> 2416[label="",style="solid", color="black", weight=3]; 2361[label="vuz350",fontsize=16,color="green",shape="box"];2362[label="vuz36",fontsize=16,color="green",shape="box"];2363[label="vuz350",fontsize=16,color="green",shape="box"];2364[label="vuz36",fontsize=16,color="green",shape="box"];2365[label="primQuotInt (primPlusInt (Neg vuz181) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (reduce2D (primPlusInt (Neg vuz182) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2365 -> 2417[label="",style="solid", color="black", weight=3]; 5754[label="gcd2 (primEqInt (primPlusInt (vuz35 * Pos (Succ vuz36)) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (vuz35 * Pos (Succ vuz36)) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5754 -> 5769[label="",style="solid", color="black", weight=3]; 2367[label="vuz400",fontsize=16,color="green",shape="box"];2368[label="vuz41",fontsize=16,color="green",shape="box"];2369[label="vuz400",fontsize=16,color="green",shape="box"];2370[label="vuz41",fontsize=16,color="green",shape="box"];2371[label="primQuotInt (primPlusInt (Neg vuz183) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (reduce2D (primPlusInt (Neg vuz184) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2371 -> 2420[label="",style="solid", color="black", weight=3]; 2372[label="vuz400",fontsize=16,color="green",shape="box"];2373[label="vuz41",fontsize=16,color="green",shape="box"];2374[label="vuz400",fontsize=16,color="green",shape="box"];2375[label="vuz41",fontsize=16,color="green",shape="box"];2376[label="primQuotInt (primPlusInt (Pos vuz189) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (reduce2D (primPlusInt (Pos vuz190) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2376 -> 2421[label="",style="solid", color="black", weight=3]; 4147[label="gcd2 (primEqInt (primPlusInt (vuz40 * Neg (Succ vuz41)) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (vuz40 * Neg (Succ vuz41)) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4147 -> 4162[label="",style="solid", color="black", weight=3]; 2378[label="vuz450",fontsize=16,color="green",shape="box"];2379[label="vuz46",fontsize=16,color="green",shape="box"];2380[label="vuz450",fontsize=16,color="green",shape="box"];2381[label="vuz46",fontsize=16,color="green",shape="box"];2382[label="primQuotInt (primPlusInt (Pos vuz191) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (reduce2D (primPlusInt (Pos vuz192) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2382 -> 2424[label="",style="solid", color="black", weight=3]; 2383[label="vuz450",fontsize=16,color="green",shape="box"];2384[label="vuz46",fontsize=16,color="green",shape="box"];2385[label="vuz450",fontsize=16,color="green",shape="box"];2386[label="vuz46",fontsize=16,color="green",shape="box"];2387[label="primQuotInt (primPlusInt (Neg vuz193) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (reduce2D (primPlusInt (Neg vuz194) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2387 -> 2425[label="",style="solid", color="black", weight=3]; 4148[label="gcd2 (primEqInt (primPlusInt (vuz45 * Pos (Succ vuz46)) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (vuz45 * Pos (Succ vuz46)) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4148 -> 4163[label="",style="solid", color="black", weight=3]; 2389[label="vuz500",fontsize=16,color="green",shape="box"];2390[label="vuz51",fontsize=16,color="green",shape="box"];2391[label="vuz500",fontsize=16,color="green",shape="box"];2392[label="vuz51",fontsize=16,color="green",shape="box"];2393[label="primQuotInt (primPlusInt (Neg vuz195) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (reduce2D (primPlusInt (Neg vuz196) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2393 -> 2428[label="",style="solid", color="black", weight=3]; 2394[label="vuz500",fontsize=16,color="green",shape="box"];2395[label="vuz51",fontsize=16,color="green",shape="box"];2396[label="vuz500",fontsize=16,color="green",shape="box"];2397[label="vuz51",fontsize=16,color="green",shape="box"];2398[label="primQuotInt (primPlusInt (Pos vuz197) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (reduce2D (primPlusInt (Pos vuz198) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2398 -> 2429[label="",style="solid", color="black", weight=3]; 5755[label="gcd2 (primEqInt (primPlusInt (vuz50 * Neg (Succ vuz51)) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (vuz50 * Neg (Succ vuz51)) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5755 -> 5770[label="",style="solid", color="black", weight=3]; 2400 -> 2432[label="",style="dashed", color="red", weight=0]; 2400[label="primQuotInt (primPlusInt (Pos vuz185) (Neg (primMulNat vuz11 (Succ vuz12)))) (reduce2D (primPlusInt (Pos vuz186) (Neg (primMulNat vuz11 (Succ vuz12)))) (Pos vuz144))",fontsize=16,color="magenta"];2400 -> 2433[label="",style="dashed", color="magenta", weight=3]; 2400 -> 2434[label="",style="dashed", color="magenta", weight=3]; 2401 -> 2440[label="",style="dashed", color="red", weight=0]; 2401[label="primQuotInt (primPlusInt (Neg vuz187) (Neg (primMulNat vuz11 (Succ vuz12)))) (reduce2D (primPlusInt (Neg vuz188) (Neg (primMulNat vuz11 (Succ vuz12)))) (Pos vuz144))",fontsize=16,color="magenta"];2401 -> 2441[label="",style="dashed", color="magenta", weight=3]; 2401 -> 2442[label="",style="dashed", color="magenta", weight=3]; 5767[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz9 (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz9 (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="burlywood",shape="box"];6502[label="vuz9/Pos vuz90",fontsize=10,color="white",style="solid",shape="box"];5767 -> 6502[label="",style="solid", color="burlywood", weight=9]; 6502 -> 5782[label="",style="solid", color="burlywood", weight=3]; 6503[label="vuz9/Neg vuz90",fontsize=10,color="white",style="solid",shape="box"];5767 -> 6503[label="",style="solid", color="burlywood", weight=9]; 6503 -> 5783[label="",style="solid", color="burlywood", weight=3]; 2404 -> 2450[label="",style="dashed", color="red", weight=0]; 2404[label="primQuotInt (primPlusInt (Neg vuz167) (Neg (primMulNat vuz22 (Succ vuz23)))) (reduce2D (primPlusInt (Neg vuz168) (Neg (primMulNat vuz22 (Succ vuz23)))) (Neg vuz68))",fontsize=16,color="magenta"];2404 -> 2451[label="",style="dashed", color="magenta", weight=3]; 2404 -> 2452[label="",style="dashed", color="magenta", weight=3]; 2405 -> 2458[label="",style="dashed", color="red", weight=0]; 2405[label="primQuotInt (primPlusInt (Pos vuz169) (Neg (primMulNat vuz22 (Succ vuz23)))) (reduce2D (primPlusInt (Pos vuz170) (Neg (primMulNat vuz22 (Succ vuz23)))) (Neg vuz68))",fontsize=16,color="magenta"];2405 -> 2459[label="",style="dashed", color="magenta", weight=3]; 2405 -> 2460[label="",style="dashed", color="magenta", weight=3]; 4158[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz20 (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz20 (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="burlywood",shape="box"];6504[label="vuz20/Pos vuz200",fontsize=10,color="white",style="solid",shape="box"];4158 -> 6504[label="",style="solid", color="burlywood", weight=9]; 6504 -> 4173[label="",style="solid", color="burlywood", weight=3]; 6505[label="vuz20/Neg vuz200",fontsize=10,color="white",style="solid",shape="box"];4158 -> 6505[label="",style="solid", color="burlywood", weight=9]; 6505 -> 4174[label="",style="solid", color="burlywood", weight=3]; 4159[label="primDivNatS0 vuz2800 vuz28100 (primGEqNatS vuz2800 vuz28100)",fontsize=16,color="burlywood",shape="box"];6506[label="vuz2800/Succ vuz28000",fontsize=10,color="white",style="solid",shape="box"];4159 -> 6506[label="",style="solid", color="burlywood", weight=9]; 6506 -> 4175[label="",style="solid", color="burlywood", weight=3]; 6507[label="vuz2800/Zero",fontsize=10,color="white",style="solid",shape="box"];4159 -> 6507[label="",style="solid", color="burlywood", weight=9]; 6507 -> 4176[label="",style="solid", color="burlywood", weight=3]; 4160[label="Zero",fontsize=16,color="green",shape="box"];2408 -> 2468[label="",style="dashed", color="red", weight=0]; 2408[label="primQuotInt (primPlusInt (Pos vuz171) (Pos (primMulNat vuz27 (Succ vuz28)))) (reduce2D (primPlusInt (Pos vuz172) (Pos (primMulNat vuz27 (Succ vuz28)))) (Neg vuz71))",fontsize=16,color="magenta"];2408 -> 2469[label="",style="dashed", color="magenta", weight=3]; 2408 -> 2470[label="",style="dashed", color="magenta", weight=3]; 2409 -> 2476[label="",style="dashed", color="red", weight=0]; 2409[label="primQuotInt (primPlusInt (Neg vuz173) (Pos (primMulNat vuz27 (Succ vuz28)))) (reduce2D (primPlusInt (Neg vuz174) (Pos (primMulNat vuz27 (Succ vuz28)))) (Neg vuz71))",fontsize=16,color="magenta"];2409 -> 2477[label="",style="dashed", color="magenta", weight=3]; 2409 -> 2478[label="",style="dashed", color="magenta", weight=3]; 4161[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz25 (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz25 (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="burlywood",shape="box"];6508[label="vuz25/Pos vuz250",fontsize=10,color="white",style="solid",shape="box"];4161 -> 6508[label="",style="solid", color="burlywood", weight=9]; 6508 -> 4177[label="",style="solid", color="burlywood", weight=3]; 6509[label="vuz25/Neg vuz250",fontsize=10,color="white",style="solid",shape="box"];4161 -> 6509[label="",style="solid", color="burlywood", weight=9]; 6509 -> 4178[label="",style="solid", color="burlywood", weight=3]; 2412 -> 2486[label="",style="dashed", color="red", weight=0]; 2412[label="primQuotInt (primPlusInt (Neg vuz175) (Pos (primMulNat vuz32 (Succ vuz33)))) (reduce2D (primPlusInt (Neg vuz176) (Pos (primMulNat vuz32 (Succ vuz33)))) (Pos vuz74))",fontsize=16,color="magenta"];2412 -> 2487[label="",style="dashed", color="magenta", weight=3]; 2412 -> 2488[label="",style="dashed", color="magenta", weight=3]; 2413 -> 2494[label="",style="dashed", color="red", weight=0]; 2413[label="primQuotInt (primPlusInt (Pos vuz177) (Pos (primMulNat vuz32 (Succ vuz33)))) (reduce2D (primPlusInt (Pos vuz178) (Pos (primMulNat vuz32 (Succ vuz33)))) (Pos vuz74))",fontsize=16,color="magenta"];2413 -> 2495[label="",style="dashed", color="magenta", weight=3]; 2413 -> 2496[label="",style="dashed", color="magenta", weight=3]; 5768[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz30 (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz30 (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="burlywood",shape="box"];6510[label="vuz30/Pos vuz300",fontsize=10,color="white",style="solid",shape="box"];5768 -> 6510[label="",style="solid", color="burlywood", weight=9]; 6510 -> 5784[label="",style="solid", color="burlywood", weight=3]; 6511[label="vuz30/Neg vuz300",fontsize=10,color="white",style="solid",shape="box"];5768 -> 6511[label="",style="solid", color="burlywood", weight=9]; 6511 -> 5785[label="",style="solid", color="burlywood", weight=3]; 2416 -> 2494[label="",style="dashed", color="red", weight=0]; 2416[label="primQuotInt (primPlusInt (Pos vuz179) (Pos (primMulNat vuz37 (Succ vuz38)))) (reduce2D (primPlusInt (Pos vuz180) (Pos (primMulNat vuz37 (Succ vuz38)))) (Pos vuz77))",fontsize=16,color="magenta"];2416 -> 2497[label="",style="dashed", color="magenta", weight=3]; 2416 -> 2498[label="",style="dashed", color="magenta", weight=3]; 2416 -> 2499[label="",style="dashed", color="magenta", weight=3]; 2416 -> 2500[label="",style="dashed", color="magenta", weight=3]; 2416 -> 2501[label="",style="dashed", color="magenta", weight=3]; 2417 -> 2486[label="",style="dashed", color="red", weight=0]; 2417[label="primQuotInt (primPlusInt (Neg vuz181) (Pos (primMulNat vuz37 (Succ vuz38)))) (reduce2D (primPlusInt (Neg vuz182) (Pos (primMulNat vuz37 (Succ vuz38)))) (Pos vuz77))",fontsize=16,color="magenta"];2417 -> 2489[label="",style="dashed", color="magenta", weight=3]; 2417 -> 2490[label="",style="dashed", color="magenta", weight=3]; 2417 -> 2491[label="",style="dashed", color="magenta", weight=3]; 2417 -> 2492[label="",style="dashed", color="magenta", weight=3]; 2417 -> 2493[label="",style="dashed", color="magenta", weight=3]; 5769[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz35 (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz35 (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ 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2482[label="",style="dashed", color="magenta", weight=3]; 2420 -> 2483[label="",style="dashed", color="magenta", weight=3]; 2421 -> 2468[label="",style="dashed", color="red", weight=0]; 2421[label="primQuotInt (primPlusInt (Pos vuz189) (Pos (primMulNat vuz42 (Succ vuz43)))) (reduce2D (primPlusInt (Pos vuz190) (Pos (primMulNat vuz42 (Succ vuz43)))) (Neg vuz92))",fontsize=16,color="magenta"];2421 -> 2471[label="",style="dashed", color="magenta", weight=3]; 2421 -> 2472[label="",style="dashed", color="magenta", weight=3]; 2421 -> 2473[label="",style="dashed", color="magenta", weight=3]; 2421 -> 2474[label="",style="dashed", color="magenta", weight=3]; 2421 -> 2475[label="",style="dashed", color="magenta", weight=3]; 4162[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz40 (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz40 (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg 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color="magenta", weight=3]; 2424 -> 2465[label="",style="dashed", color="magenta", weight=3]; 2425 -> 2450[label="",style="dashed", color="red", weight=0]; 2425[label="primQuotInt (primPlusInt (Neg vuz193) (Neg (primMulNat vuz47 (Succ vuz48)))) (reduce2D (primPlusInt (Neg vuz194) (Neg (primMulNat vuz47 (Succ vuz48)))) (Neg vuz107))",fontsize=16,color="magenta"];2425 -> 2453[label="",style="dashed", color="magenta", weight=3]; 2425 -> 2454[label="",style="dashed", color="magenta", weight=3]; 2425 -> 2455[label="",style="dashed", color="magenta", weight=3]; 2425 -> 2456[label="",style="dashed", color="magenta", weight=3]; 2425 -> 2457[label="",style="dashed", color="magenta", weight=3]; 4163[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz45 (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz45 (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="burlywood",shape="box"];6516[label="vuz45/Pos vuz450",fontsize=10,color="white",style="solid",shape="box"];4163 -> 6516[label="",style="solid", color="burlywood", weight=9]; 6516 -> 4181[label="",style="solid", color="burlywood", weight=3]; 6517[label="vuz45/Neg vuz450",fontsize=10,color="white",style="solid",shape="box"];4163 -> 6517[label="",style="solid", color="burlywood", weight=9]; 6517 -> 4182[label="",style="solid", color="burlywood", weight=3]; 2428 -> 2440[label="",style="dashed", color="red", weight=0]; 2428[label="primQuotInt (primPlusInt (Neg vuz195) (Neg (primMulNat vuz52 (Succ vuz53)))) (reduce2D (primPlusInt (Neg vuz196) (Neg (primMulNat vuz52 (Succ vuz53)))) (Pos vuz122))",fontsize=16,color="magenta"];2428 -> 2443[label="",style="dashed", color="magenta", weight=3]; 2428 -> 2444[label="",style="dashed", color="magenta", weight=3]; 2428 -> 2445[label="",style="dashed", color="magenta", weight=3]; 2428 -> 2446[label="",style="dashed", color="magenta", weight=3]; 2428 -> 2447[label="",style="dashed", color="magenta", weight=3]; 2429 -> 2432[label="",style="dashed", color="red", weight=0]; 2429[label="primQuotInt (primPlusInt (Pos vuz197) (Neg (primMulNat vuz52 (Succ vuz53)))) (reduce2D (primPlusInt (Pos vuz198) (Neg (primMulNat vuz52 (Succ vuz53)))) (Pos vuz122))",fontsize=16,color="magenta"];2429 -> 2435[label="",style="dashed", color="magenta", weight=3]; 2429 -> 2436[label="",style="dashed", color="magenta", weight=3]; 2429 -> 2437[label="",style="dashed", color="magenta", weight=3]; 2429 -> 2438[label="",style="dashed", color="magenta", weight=3]; 2429 -> 2439[label="",style="dashed", color="magenta", weight=3]; 5770[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz50 (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz50 (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="burlywood",shape="box"];6518[label="vuz50/Pos vuz500",fontsize=10,color="white",style="solid",shape="box"];5770 -> 6518[label="",style="solid", color="burlywood", weight=9]; 6518 -> 5788[label="",style="solid", color="burlywood", weight=3]; 6519[label="vuz50/Neg vuz500",fontsize=10,color="white",style="solid",shape="box"];5770 -> 6519[label="",style="solid", color="burlywood", weight=9]; 6519 -> 5789[label="",style="solid", color="burlywood", weight=3]; 2433 -> 678[label="",style="dashed", color="red", weight=0]; 2433[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];2433 -> 2512[label="",style="dashed", color="magenta", weight=3]; 2433 -> 2513[label="",style="dashed", color="magenta", weight=3]; 2434 -> 678[label="",style="dashed", color="red", weight=0]; 2434[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];2434 -> 2514[label="",style="dashed", color="magenta", weight=3]; 2434 -> 2515[label="",style="dashed", color="magenta", weight=3]; 2432[label="primQuotInt (primPlusInt (Pos vuz185) (Neg vuz199)) (reduce2D (primPlusInt (Pos vuz186) (Neg vuz200)) (Pos vuz144))",fontsize=16,color="black",shape="triangle"];2432 -> 2516[label="",style="solid", color="black", weight=3]; 2441 -> 678[label="",style="dashed", color="red", weight=0]; 2441[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];2441 -> 2517[label="",style="dashed", color="magenta", weight=3]; 2441 -> 2518[label="",style="dashed", color="magenta", weight=3]; 2442 -> 678[label="",style="dashed", color="red", weight=0]; 2442[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];2442 -> 2519[label="",style="dashed", color="magenta", weight=3]; 2442 -> 2520[label="",style="dashed", color="magenta", weight=3]; 2440[label="primQuotInt (primPlusInt (Neg vuz187) (Neg vuz201)) (reduce2D (primPlusInt (Neg vuz188) (Neg vuz202)) (Pos vuz144))",fontsize=16,color="black",shape="triangle"];2440 -> 2521[label="",style="solid", color="black", weight=3]; 5782[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5782 -> 5804[label="",style="solid", color="black", weight=3]; 5783[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5783 -> 5805[label="",style="solid", color="black", weight=3]; 2451 -> 678[label="",style="dashed", color="red", weight=0]; 2451[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];2451 -> 2528[label="",style="dashed", color="magenta", weight=3]; 2451 -> 2529[label="",style="dashed", color="magenta", weight=3]; 2452 -> 678[label="",style="dashed", color="red", weight=0]; 2452[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];2452 -> 2530[label="",style="dashed", color="magenta", weight=3]; 2452 -> 2531[label="",style="dashed", color="magenta", weight=3]; 2450[label="primQuotInt (primPlusInt (Neg vuz167) (Neg vuz203)) (reduce2D (primPlusInt (Neg vuz168) (Neg vuz204)) (Neg vuz68))",fontsize=16,color="black",shape="triangle"];2450 -> 2532[label="",style="solid", color="black", weight=3]; 2459 -> 678[label="",style="dashed", color="red", weight=0]; 2459[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];2459 -> 2533[label="",style="dashed", color="magenta", weight=3]; 2459 -> 2534[label="",style="dashed", color="magenta", weight=3]; 2460 -> 678[label="",style="dashed", color="red", weight=0]; 2460[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];2460 -> 2535[label="",style="dashed", color="magenta", weight=3]; 2460 -> 2536[label="",style="dashed", color="magenta", weight=3]; 2458[label="primQuotInt (primPlusInt (Pos vuz169) (Neg vuz205)) (reduce2D (primPlusInt (Pos vuz170) (Neg vuz206)) (Neg vuz68))",fontsize=16,color="black",shape="triangle"];2458 -> 2537[label="",style="solid", color="black", weight=3]; 4173[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4173 -> 4192[label="",style="solid", color="black", weight=3]; 4174[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4174 -> 4193[label="",style="solid", color="black", weight=3]; 4175[label="primDivNatS0 (Succ vuz28000) vuz28100 (primGEqNatS (Succ vuz28000) vuz28100)",fontsize=16,color="burlywood",shape="box"];6520[label="vuz28100/Succ vuz281000",fontsize=10,color="white",style="solid",shape="box"];4175 -> 6520[label="",style="solid", color="burlywood", weight=9]; 6520 -> 4194[label="",style="solid", color="burlywood", weight=3]; 6521[label="vuz28100/Zero",fontsize=10,color="white",style="solid",shape="box"];4175 -> 6521[label="",style="solid", color="burlywood", weight=9]; 6521 -> 4195[label="",style="solid", color="burlywood", weight=3]; 4176[label="primDivNatS0 Zero vuz28100 (primGEqNatS Zero vuz28100)",fontsize=16,color="burlywood",shape="box"];6522[label="vuz28100/Succ vuz281000",fontsize=10,color="white",style="solid",shape="box"];4176 -> 6522[label="",style="solid", color="burlywood", weight=9]; 6522 -> 4196[label="",style="solid", color="burlywood", weight=3]; 6523[label="vuz28100/Zero",fontsize=10,color="white",style="solid",shape="box"];4176 -> 6523[label="",style="solid", color="burlywood", weight=9]; 6523 -> 4197[label="",style="solid", color="burlywood", weight=3]; 2469 -> 678[label="",style="dashed", color="red", weight=0]; 2469[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];2469 -> 2544[label="",style="dashed", color="magenta", weight=3]; 2469 -> 2545[label="",style="dashed", color="magenta", weight=3]; 2470 -> 678[label="",style="dashed", color="red", weight=0]; 2470[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];2470 -> 2546[label="",style="dashed", color="magenta", weight=3]; 2470 -> 2547[label="",style="dashed", color="magenta", weight=3]; 2468[label="primQuotInt (primPlusInt (Pos vuz171) (Pos vuz207)) (reduce2D (primPlusInt (Pos vuz172) (Pos vuz208)) (Neg vuz71))",fontsize=16,color="black",shape="triangle"];2468 -> 2548[label="",style="solid", color="black", weight=3]; 2477 -> 678[label="",style="dashed", color="red", weight=0]; 2477[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];2477 -> 2549[label="",style="dashed", color="magenta", weight=3]; 2477 -> 2550[label="",style="dashed", color="magenta", weight=3]; 2478 -> 678[label="",style="dashed", color="red", weight=0]; 2478[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];2478 -> 2551[label="",style="dashed", color="magenta", weight=3]; 2478 -> 2552[label="",style="dashed", color="magenta", weight=3]; 2476[label="primQuotInt (primPlusInt (Neg vuz173) (Pos vuz209)) (reduce2D (primPlusInt (Neg vuz174) (Pos vuz210)) (Neg vuz71))",fontsize=16,color="black",shape="triangle"];2476 -> 2553[label="",style="solid", color="black", weight=3]; 4177[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4177 -> 4198[label="",style="solid", color="black", weight=3]; 4178[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4178 -> 4199[label="",style="solid", color="black", weight=3]; 2487 -> 678[label="",style="dashed", color="red", weight=0]; 2487[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];2487 -> 2560[label="",style="dashed", color="magenta", weight=3]; 2487 -> 2561[label="",style="dashed", color="magenta", weight=3]; 2488 -> 678[label="",style="dashed", color="red", weight=0]; 2488[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];2488 -> 2562[label="",style="dashed", color="magenta", weight=3]; 2488 -> 2563[label="",style="dashed", color="magenta", weight=3]; 2486[label="primQuotInt (primPlusInt (Neg vuz175) (Pos vuz211)) (reduce2D (primPlusInt (Neg vuz176) (Pos vuz212)) (Pos vuz74))",fontsize=16,color="black",shape="triangle"];2486 -> 2564[label="",style="solid", color="black", weight=3]; 2495 -> 678[label="",style="dashed", color="red", weight=0]; 2495[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];2495 -> 2565[label="",style="dashed", color="magenta", weight=3]; 2495 -> 2566[label="",style="dashed", color="magenta", weight=3]; 2496 -> 678[label="",style="dashed", color="red", weight=0]; 2496[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];2496 -> 2567[label="",style="dashed", color="magenta", weight=3]; 2496 -> 2568[label="",style="dashed", color="magenta", weight=3]; 2494[label="primQuotInt (primPlusInt (Pos vuz177) (Pos vuz213)) (reduce2D (primPlusInt (Pos vuz178) (Pos vuz214)) (Pos vuz74))",fontsize=16,color="black",shape="triangle"];2494 -> 2569[label="",style="solid", color="black", weight=3]; 5784[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5784 -> 5806[label="",style="solid", color="black", weight=3]; 5785[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5785 -> 5807[label="",style="solid", color="black", weight=3]; 2497 -> 678[label="",style="dashed", color="red", weight=0]; 2497[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];2497 -> 2576[label="",style="dashed", color="magenta", weight=3]; 2497 -> 2577[label="",style="dashed", color="magenta", weight=3]; 2498[label="vuz77",fontsize=16,color="green",shape="box"];2499[label="vuz179",fontsize=16,color="green",shape="box"];2500[label="vuz180",fontsize=16,color="green",shape="box"];2501 -> 678[label="",style="dashed", color="red", weight=0]; 2501[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];2501 -> 2578[label="",style="dashed", color="magenta", weight=3]; 2501 -> 2579[label="",style="dashed", color="magenta", weight=3]; 2489 -> 678[label="",style="dashed", color="red", weight=0]; 2489[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];2489 -> 2580[label="",style="dashed", color="magenta", weight=3]; 2489 -> 2581[label="",style="dashed", color="magenta", weight=3]; 2490[label="vuz182",fontsize=16,color="green",shape="box"];2491[label="vuz77",fontsize=16,color="green",shape="box"];2492 -> 678[label="",style="dashed", color="red", weight=0]; 2492[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];2492 -> 2582[label="",style="dashed", color="magenta", weight=3]; 2492 -> 2583[label="",style="dashed", color="magenta", weight=3]; 2493[label="vuz181",fontsize=16,color="green",shape="box"];5786[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5786 -> 5808[label="",style="solid", color="black", weight=3]; 5787[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5787 -> 5809[label="",style="solid", color="black", weight=3]; 2479 -> 678[label="",style="dashed", color="red", weight=0]; 2479[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];2479 -> 2590[label="",style="dashed", color="magenta", weight=3]; 2479 -> 2591[label="",style="dashed", color="magenta", weight=3]; 2480[label="vuz92",fontsize=16,color="green",shape="box"];2481[label="vuz183",fontsize=16,color="green",shape="box"];2482 -> 678[label="",style="dashed", color="red", weight=0]; 2482[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];2482 -> 2592[label="",style="dashed", color="magenta", weight=3]; 2482 -> 2593[label="",style="dashed", color="magenta", weight=3]; 2483[label="vuz184",fontsize=16,color="green",shape="box"];2471[label="vuz190",fontsize=16,color="green",shape="box"];2472[label="vuz189",fontsize=16,color="green",shape="box"];2473[label="vuz92",fontsize=16,color="green",shape="box"];2474 -> 678[label="",style="dashed", color="red", weight=0]; 2474[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];2474 -> 2594[label="",style="dashed", color="magenta", weight=3]; 2474 -> 2595[label="",style="dashed", color="magenta", weight=3]; 2475 -> 678[label="",style="dashed", color="red", weight=0]; 2475[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];2475 -> 2596[label="",style="dashed", color="magenta", weight=3]; 2475 -> 2597[label="",style="dashed", color="magenta", weight=3]; 4179[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4179 -> 4200[label="",style="solid", color="black", weight=3]; 4180[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4180 -> 4201[label="",style="solid", color="black", weight=3]; 2461[label="vuz192",fontsize=16,color="green",shape="box"];2462 -> 678[label="",style="dashed", color="red", weight=0]; 2462[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];2462 -> 2604[label="",style="dashed", color="magenta", weight=3]; 2462 -> 2605[label="",style="dashed", color="magenta", weight=3]; 2463 -> 678[label="",style="dashed", color="red", weight=0]; 2463[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];2463 -> 2606[label="",style="dashed", color="magenta", weight=3]; 2463 -> 2607[label="",style="dashed", color="magenta", weight=3]; 2464[label="vuz107",fontsize=16,color="green",shape="box"];2465[label="vuz191",fontsize=16,color="green",shape="box"];2453 -> 678[label="",style="dashed", color="red", weight=0]; 2453[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];2453 -> 2608[label="",style="dashed", color="magenta", weight=3]; 2453 -> 2609[label="",style="dashed", color="magenta", weight=3]; 2454[label="vuz194",fontsize=16,color="green",shape="box"];2455[label="vuz193",fontsize=16,color="green",shape="box"];2456[label="vuz107",fontsize=16,color="green",shape="box"];2457 -> 678[label="",style="dashed", color="red", weight=0]; 2457[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];2457 -> 2610[label="",style="dashed", color="magenta", weight=3]; 2457 -> 2611[label="",style="dashed", color="magenta", weight=3]; 4181[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4181 -> 4202[label="",style="solid", color="black", weight=3]; 4182[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4182 -> 4203[label="",style="solid", color="black", weight=3]; 2443 -> 678[label="",style="dashed", color="red", weight=0]; 2443[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];2443 -> 2618[label="",style="dashed", color="magenta", weight=3]; 2443 -> 2619[label="",style="dashed", color="magenta", weight=3]; 2444[label="vuz196",fontsize=16,color="green",shape="box"];2445[label="vuz195",fontsize=16,color="green",shape="box"];2446 -> 678[label="",style="dashed", color="red", weight=0]; 2446[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];2446 -> 2620[label="",style="dashed", color="magenta", weight=3]; 2446 -> 2621[label="",style="dashed", color="magenta", weight=3]; 2447[label="vuz122",fontsize=16,color="green",shape="box"];2435[label="vuz198",fontsize=16,color="green",shape="box"];2436 -> 678[label="",style="dashed", color="red", weight=0]; 2436[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];2436 -> 2622[label="",style="dashed", color="magenta", weight=3]; 2436 -> 2623[label="",style="dashed", color="magenta", weight=3]; 2437 -> 678[label="",style="dashed", color="red", weight=0]; 2437[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];2437 -> 2624[label="",style="dashed", color="magenta", weight=3]; 2437 -> 2625[label="",style="dashed", color="magenta", weight=3]; 2438[label="vuz122",fontsize=16,color="green",shape="box"];2439[label="vuz197",fontsize=16,color="green",shape="box"];5788[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5788 -> 5810[label="",style="solid", color="black", weight=3]; 5789[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5789 -> 5811[label="",style="solid", color="black", weight=3]; 2512[label="vuz11",fontsize=16,color="green",shape="box"];2513[label="vuz12",fontsize=16,color="green",shape="box"];2514[label="vuz11",fontsize=16,color="green",shape="box"];2515[label="vuz12",fontsize=16,color="green",shape="box"];2516[label="primQuotInt (primMinusNat vuz185 vuz199) (reduce2D (primMinusNat vuz185 vuz199) (Pos vuz144))",fontsize=16,color="burlywood",shape="triangle"];6524[label="vuz185/Succ vuz1850",fontsize=10,color="white",style="solid",shape="box"];2516 -> 6524[label="",style="solid", color="burlywood", weight=9]; 6524 -> 2632[label="",style="solid", color="burlywood", weight=3]; 6525[label="vuz185/Zero",fontsize=10,color="white",style="solid",shape="box"];2516 -> 6525[label="",style="solid", color="burlywood", weight=9]; 6525 -> 2633[label="",style="solid", color="burlywood", weight=3]; 2517[label="vuz11",fontsize=16,color="green",shape="box"];2518[label="vuz12",fontsize=16,color="green",shape="box"];2519[label="vuz11",fontsize=16,color="green",shape="box"];2520[label="vuz12",fontsize=16,color="green",shape="box"];2521 -> 3507[label="",style="dashed", color="red", weight=0]; 2521[label="primQuotInt (Neg (primPlusNat vuz187 vuz201)) (reduce2D (Neg (primPlusNat vuz187 vuz201)) (Pos vuz144))",fontsize=16,color="magenta"];2521 -> 3580[label="",style="dashed", color="magenta", weight=3]; 2521 -> 3581[label="",style="dashed", color="magenta", weight=3]; 5804 -> 5824[label="",style="dashed", color="red", weight=0]; 5804[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="magenta"];5804 -> 5825[label="",style="dashed", color="magenta", weight=3]; 5804 -> 5826[label="",style="dashed", color="magenta", weight=3]; 5805 -> 5827[label="",style="dashed", color="red", weight=0]; 5805[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="magenta"];5805 -> 5828[label="",style="dashed", color="magenta", weight=3]; 5805 -> 5829[label="",style="dashed", color="magenta", weight=3]; 2528[label="vuz22",fontsize=16,color="green",shape="box"];2529[label="vuz23",fontsize=16,color="green",shape="box"];2530[label="vuz22",fontsize=16,color="green",shape="box"];2531[label="vuz23",fontsize=16,color="green",shape="box"];2532 -> 3507[label="",style="dashed", color="red", weight=0]; 2532[label="primQuotInt (Neg (primPlusNat vuz167 vuz203)) (reduce2D (Neg (primPlusNat vuz167 vuz203)) (Neg vuz68))",fontsize=16,color="magenta"];2532 -> 3582[label="",style="dashed", color="magenta", weight=3]; 2532 -> 3583[label="",style="dashed", color="magenta", weight=3]; 2533[label="vuz22",fontsize=16,color="green",shape="box"];2534[label="vuz23",fontsize=16,color="green",shape="box"];2535[label="vuz22",fontsize=16,color="green",shape="box"];2536[label="vuz23",fontsize=16,color="green",shape="box"];2537[label="primQuotInt (primMinusNat vuz169 vuz205) (reduce2D (primMinusNat vuz169 vuz205) (Neg vuz68))",fontsize=16,color="burlywood",shape="triangle"];6526[label="vuz169/Succ vuz1690",fontsize=10,color="white",style="solid",shape="box"];2537 -> 6526[label="",style="solid", color="burlywood", weight=9]; 6526 -> 2650[label="",style="solid", color="burlywood", weight=3]; 6527[label="vuz169/Zero",fontsize=10,color="white",style="solid",shape="box"];2537 -> 6527[label="",style="solid", color="burlywood", weight=9]; 6527 -> 2651[label="",style="solid", color="burlywood", weight=3]; 4192 -> 4214[label="",style="dashed", color="red", weight=0]; 4192[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="magenta"];4192 -> 4215[label="",style="dashed", color="magenta", weight=3]; 4192 -> 4216[label="",style="dashed", color="magenta", weight=3]; 4193 -> 4217[label="",style="dashed", color="red", weight=0]; 4193[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="magenta"];4193 -> 4218[label="",style="dashed", color="magenta", weight=3]; 4193 -> 4219[label="",style="dashed", color="magenta", weight=3]; 4194[label="primDivNatS0 (Succ vuz28000) (Succ vuz281000) (primGEqNatS (Succ vuz28000) (Succ vuz281000))",fontsize=16,color="black",shape="box"];4194 -> 4220[label="",style="solid", color="black", weight=3]; 4195[label="primDivNatS0 (Succ vuz28000) Zero (primGEqNatS (Succ vuz28000) Zero)",fontsize=16,color="black",shape="box"];4195 -> 4221[label="",style="solid", color="black", weight=3]; 4196[label="primDivNatS0 Zero (Succ vuz281000) (primGEqNatS Zero (Succ vuz281000))",fontsize=16,color="black",shape="box"];4196 -> 4222[label="",style="solid", color="black", weight=3]; 4197[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];4197 -> 4223[label="",style="solid", color="black", weight=3]; 2544[label="vuz27",fontsize=16,color="green",shape="box"];2545[label="vuz28",fontsize=16,color="green",shape="box"];2546[label="vuz27",fontsize=16,color="green",shape="box"];2547[label="vuz28",fontsize=16,color="green",shape="box"];2548 -> 5044[label="",style="dashed", color="red", weight=0]; 2548[label="primQuotInt (Pos (primPlusNat vuz171 vuz207)) (reduce2D (Pos (primPlusNat vuz171 vuz207)) (Neg vuz71))",fontsize=16,color="magenta"];2548 -> 5112[label="",style="dashed", color="magenta", weight=3]; 2548 -> 5113[label="",style="dashed", color="magenta", weight=3]; 2549[label="vuz27",fontsize=16,color="green",shape="box"];2550[label="vuz28",fontsize=16,color="green",shape="box"];2551[label="vuz27",fontsize=16,color="green",shape="box"];2552[label="vuz28",fontsize=16,color="green",shape="box"];2553 -> 2537[label="",style="dashed", color="red", weight=0]; 2553[label="primQuotInt (primMinusNat vuz209 vuz173) (reduce2D (primMinusNat vuz209 vuz173) (Neg vuz71))",fontsize=16,color="magenta"];2553 -> 2665[label="",style="dashed", color="magenta", weight=3]; 2553 -> 2666[label="",style="dashed", color="magenta", weight=3]; 2553 -> 2667[label="",style="dashed", color="magenta", weight=3]; 4198 -> 4224[label="",style="dashed", color="red", weight=0]; 4198[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="magenta"];4198 -> 4225[label="",style="dashed", color="magenta", weight=3]; 4198 -> 4226[label="",style="dashed", color="magenta", weight=3]; 4199 -> 4227[label="",style="dashed", color="red", weight=0]; 4199[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="magenta"];4199 -> 4228[label="",style="dashed", color="magenta", weight=3]; 4199 -> 4229[label="",style="dashed", color="magenta", weight=3]; 2560[label="vuz32",fontsize=16,color="green",shape="box"];2561[label="vuz33",fontsize=16,color="green",shape="box"];2562[label="vuz32",fontsize=16,color="green",shape="box"];2563[label="vuz33",fontsize=16,color="green",shape="box"];2564 -> 2516[label="",style="dashed", color="red", weight=0]; 2564[label="primQuotInt (primMinusNat vuz211 vuz175) (reduce2D (primMinusNat vuz211 vuz175) (Pos vuz74))",fontsize=16,color="magenta"];2564 -> 2678[label="",style="dashed", color="magenta", weight=3]; 2564 -> 2679[label="",style="dashed", color="magenta", weight=3]; 2564 -> 2680[label="",style="dashed", color="magenta", weight=3]; 2565[label="vuz32",fontsize=16,color="green",shape="box"];2566[label="vuz33",fontsize=16,color="green",shape="box"];2567[label="vuz32",fontsize=16,color="green",shape="box"];2568[label="vuz33",fontsize=16,color="green",shape="box"];2569 -> 5044[label="",style="dashed", color="red", weight=0]; 2569[label="primQuotInt (Pos (primPlusNat vuz177 vuz213)) (reduce2D (Pos (primPlusNat vuz177 vuz213)) (Pos vuz74))",fontsize=16,color="magenta"];2569 -> 5114[label="",style="dashed", color="magenta", weight=3]; 2569 -> 5115[label="",style="dashed", color="magenta", weight=3]; 5806 -> 5830[label="",style="dashed", color="red", weight=0]; 5806[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="magenta"];5806 -> 5831[label="",style="dashed", color="magenta", weight=3]; 5806 -> 5832[label="",style="dashed", color="magenta", weight=3]; 5807 -> 5833[label="",style="dashed", color="red", weight=0]; 5807[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="magenta"];5807 -> 5834[label="",style="dashed", color="magenta", weight=3]; 5807 -> 5835[label="",style="dashed", color="magenta", weight=3]; 2576[label="vuz37",fontsize=16,color="green",shape="box"];2577[label="vuz38",fontsize=16,color="green",shape="box"];2578[label="vuz37",fontsize=16,color="green",shape="box"];2579[label="vuz38",fontsize=16,color="green",shape="box"];2580[label="vuz37",fontsize=16,color="green",shape="box"];2581[label="vuz38",fontsize=16,color="green",shape="box"];2582[label="vuz37",fontsize=16,color="green",shape="box"];2583[label="vuz38",fontsize=16,color="green",shape="box"];5808 -> 5836[label="",style="dashed", color="red", weight=0]; 5808[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="magenta"];5808 -> 5837[label="",style="dashed", color="magenta", weight=3]; 5808 -> 5838[label="",style="dashed", color="magenta", weight=3]; 5809 -> 5839[label="",style="dashed", color="red", weight=0]; 5809[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="magenta"];5809 -> 5840[label="",style="dashed", color="magenta", weight=3]; 5809 -> 5841[label="",style="dashed", color="magenta", weight=3]; 2590[label="vuz42",fontsize=16,color="green",shape="box"];2591[label="vuz43",fontsize=16,color="green",shape="box"];2592[label="vuz42",fontsize=16,color="green",shape="box"];2593[label="vuz43",fontsize=16,color="green",shape="box"];2594[label="vuz42",fontsize=16,color="green",shape="box"];2595[label="vuz43",fontsize=16,color="green",shape="box"];2596[label="vuz42",fontsize=16,color="green",shape="box"];2597[label="vuz43",fontsize=16,color="green",shape="box"];4200 -> 4230[label="",style="dashed", color="red", weight=0]; 4200[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="magenta"];4200 -> 4231[label="",style="dashed", color="magenta", weight=3]; 4200 -> 4232[label="",style="dashed", color="magenta", weight=3]; 4201 -> 4233[label="",style="dashed", color="red", weight=0]; 4201[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="magenta"];4201 -> 4234[label="",style="dashed", color="magenta", weight=3]; 4201 -> 4235[label="",style="dashed", color="magenta", weight=3]; 2604[label="vuz47",fontsize=16,color="green",shape="box"];2605[label="vuz48",fontsize=16,color="green",shape="box"];2606[label="vuz47",fontsize=16,color="green",shape="box"];2607[label="vuz48",fontsize=16,color="green",shape="box"];2608[label="vuz47",fontsize=16,color="green",shape="box"];2609[label="vuz48",fontsize=16,color="green",shape="box"];2610[label="vuz47",fontsize=16,color="green",shape="box"];2611[label="vuz48",fontsize=16,color="green",shape="box"];4202 -> 4236[label="",style="dashed", color="red", weight=0]; 4202[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="magenta"];4202 -> 4237[label="",style="dashed", color="magenta", weight=3]; 4202 -> 4238[label="",style="dashed", color="magenta", weight=3]; 4203 -> 4239[label="",style="dashed", color="red", weight=0]; 4203[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="magenta"];4203 -> 4240[label="",style="dashed", color="magenta", weight=3]; 4203 -> 4241[label="",style="dashed", color="magenta", weight=3]; 2618[label="vuz52",fontsize=16,color="green",shape="box"];2619[label="vuz53",fontsize=16,color="green",shape="box"];2620[label="vuz52",fontsize=16,color="green",shape="box"];2621[label="vuz53",fontsize=16,color="green",shape="box"];2622[label="vuz52",fontsize=16,color="green",shape="box"];2623[label="vuz53",fontsize=16,color="green",shape="box"];2624[label="vuz52",fontsize=16,color="green",shape="box"];2625[label="vuz53",fontsize=16,color="green",shape="box"];5810 -> 5842[label="",style="dashed", color="red", weight=0]; 5810[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="magenta"];5810 -> 5843[label="",style="dashed", color="magenta", weight=3]; 5810 -> 5844[label="",style="dashed", color="magenta", weight=3]; 5811 -> 5845[label="",style="dashed", color="red", weight=0]; 5811[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="magenta"];5811 -> 5846[label="",style="dashed", color="magenta", weight=3]; 5811 -> 5847[label="",style="dashed", color="magenta", weight=3]; 2632[label="primQuotInt (primMinusNat (Succ vuz1850) vuz199) (reduce2D (primMinusNat (Succ vuz1850) vuz199) (Pos vuz144))",fontsize=16,color="burlywood",shape="box"];6528[label="vuz199/Succ vuz1990",fontsize=10,color="white",style="solid",shape="box"];2632 -> 6528[label="",style="solid", color="burlywood", weight=9]; 6528 -> 2734[label="",style="solid", color="burlywood", weight=3]; 6529[label="vuz199/Zero",fontsize=10,color="white",style="solid",shape="box"];2632 -> 6529[label="",style="solid", color="burlywood", weight=9]; 6529 -> 2735[label="",style="solid", color="burlywood", weight=3]; 2633[label="primQuotInt (primMinusNat Zero vuz199) (reduce2D (primMinusNat Zero vuz199) (Pos vuz144))",fontsize=16,color="burlywood",shape="box"];6530[label="vuz199/Succ vuz1990",fontsize=10,color="white",style="solid",shape="box"];2633 -> 6530[label="",style="solid", color="burlywood", weight=9]; 6530 -> 2736[label="",style="solid", color="burlywood", weight=3]; 6531[label="vuz199/Zero",fontsize=10,color="white",style="solid",shape="box"];2633 -> 6531[label="",style="solid", color="burlywood", weight=9]; 6531 -> 2737[label="",style="solid", color="burlywood", weight=3]; 3580 -> 4088[label="",style="dashed", color="red", weight=0]; 3580[label="reduce2D (Neg (primPlusNat vuz187 vuz201)) (Pos vuz144)",fontsize=16,color="magenta"];3580 -> 4089[label="",style="dashed", color="magenta", weight=3]; 3581 -> 1352[label="",style="dashed", color="red", weight=0]; 3581[label="primPlusNat vuz187 vuz201",fontsize=16,color="magenta"];3581 -> 4099[label="",style="dashed", color="magenta", weight=3]; 3581 -> 4100[label="",style="dashed", color="magenta", weight=3]; 5825 -> 678[label="",style="dashed", color="red", weight=0]; 5825[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];5825 -> 5848[label="",style="dashed", color="magenta", weight=3]; 5825 -> 5849[label="",style="dashed", color="magenta", weight=3]; 5826 -> 678[label="",style="dashed", color="red", weight=0]; 5826[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];5826 -> 5850[label="",style="dashed", color="magenta", weight=3]; 5826 -> 5851[label="",style="dashed", color="magenta", weight=3]; 5824[label="gcd2 (primEqInt (primPlusInt (Pos vuz350) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz349) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];5824 -> 5852[label="",style="solid", color="black", weight=3]; 5828 -> 678[label="",style="dashed", color="red", weight=0]; 5828[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];5828 -> 5853[label="",style="dashed", color="magenta", weight=3]; 5828 -> 5854[label="",style="dashed", color="magenta", weight=3]; 5829 -> 678[label="",style="dashed", color="red", weight=0]; 5829[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];5829 -> 5855[label="",style="dashed", color="magenta", weight=3]; 5829 -> 5856[label="",style="dashed", color="magenta", weight=3]; 5827[label="gcd2 (primEqInt (primPlusInt (Neg vuz352) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz351) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];5827 -> 5857[label="",style="solid", color="black", weight=3]; 3582 -> 4101[label="",style="dashed", color="red", weight=0]; 3582[label="reduce2D (Neg (primPlusNat vuz167 vuz203)) (Neg vuz68)",fontsize=16,color="magenta"];3582 -> 4102[label="",style="dashed", color="magenta", weight=3]; 3583 -> 1352[label="",style="dashed", color="red", weight=0]; 3583[label="primPlusNat vuz167 vuz203",fontsize=16,color="magenta"];3583 -> 4112[label="",style="dashed", color="magenta", weight=3]; 3583 -> 4113[label="",style="dashed", color="magenta", weight=3]; 2650[label="primQuotInt (primMinusNat (Succ vuz1690) vuz205) (reduce2D (primMinusNat (Succ vuz1690) vuz205) (Neg vuz68))",fontsize=16,color="burlywood",shape="box"];6532[label="vuz205/Succ vuz2050",fontsize=10,color="white",style="solid",shape="box"];2650 -> 6532[label="",style="solid", color="burlywood", weight=9]; 6532 -> 2750[label="",style="solid", color="burlywood", weight=3]; 6533[label="vuz205/Zero",fontsize=10,color="white",style="solid",shape="box"];2650 -> 6533[label="",style="solid", color="burlywood", weight=9]; 6533 -> 2751[label="",style="solid", color="burlywood", weight=3]; 2651[label="primQuotInt (primMinusNat Zero vuz205) (reduce2D (primMinusNat Zero vuz205) (Neg vuz68))",fontsize=16,color="burlywood",shape="box"];6534[label="vuz205/Succ vuz2050",fontsize=10,color="white",style="solid",shape="box"];2651 -> 6534[label="",style="solid", color="burlywood", weight=9]; 6534 -> 2752[label="",style="solid", color="burlywood", weight=3]; 6535[label="vuz205/Zero",fontsize=10,color="white",style="solid",shape="box"];2651 -> 6535[label="",style="solid", color="burlywood", weight=9]; 6535 -> 2753[label="",style="solid", color="burlywood", weight=3]; 4215 -> 678[label="",style="dashed", color="red", weight=0]; 4215[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];4215 -> 4242[label="",style="dashed", color="magenta", weight=3]; 4215 -> 4243[label="",style="dashed", color="magenta", weight=3]; 4216 -> 678[label="",style="dashed", color="red", weight=0]; 4216[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];4216 -> 4244[label="",style="dashed", color="magenta", weight=3]; 4216 -> 4245[label="",style="dashed", color="magenta", weight=3]; 4214[label="gcd2 (primEqInt (primPlusInt (Neg vuz285) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz284) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4214 -> 4246[label="",style="solid", color="black", weight=3]; 4218 -> 678[label="",style="dashed", color="red", weight=0]; 4218[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];4218 -> 4247[label="",style="dashed", color="magenta", weight=3]; 4218 -> 4248[label="",style="dashed", color="magenta", weight=3]; 4219 -> 678[label="",style="dashed", color="red", weight=0]; 4219[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];4219 -> 4249[label="",style="dashed", color="magenta", weight=3]; 4219 -> 4250[label="",style="dashed", color="magenta", weight=3]; 4217[label="gcd2 (primEqInt (primPlusInt (Pos vuz287) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz286) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4217 -> 4251[label="",style="solid", color="black", weight=3]; 4220 -> 4925[label="",style="dashed", color="red", weight=0]; 4220[label="primDivNatS0 (Succ vuz28000) (Succ vuz281000) (primGEqNatS vuz28000 vuz281000)",fontsize=16,color="magenta"];4220 -> 4926[label="",style="dashed", color="magenta", weight=3]; 4220 -> 4927[label="",style="dashed", color="magenta", weight=3]; 4220 -> 4928[label="",style="dashed", color="magenta", weight=3]; 4220 -> 4929[label="",style="dashed", color="magenta", weight=3]; 4221[label="primDivNatS0 (Succ vuz28000) Zero True",fontsize=16,color="black",shape="box"];4221 -> 4254[label="",style="solid", color="black", weight=3]; 4222[label="primDivNatS0 Zero (Succ vuz281000) False",fontsize=16,color="black",shape="box"];4222 -> 4255[label="",style="solid", color="black", weight=3]; 4223[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];4223 -> 4256[label="",style="solid", color="black", weight=3]; 5112 -> 1352[label="",style="dashed", color="red", weight=0]; 5112[label="primPlusNat vuz171 vuz207",fontsize=16,color="magenta"];5112 -> 5687[label="",style="dashed", color="magenta", weight=3]; 5112 -> 5688[label="",style="dashed", color="magenta", weight=3]; 5113 -> 5689[label="",style="dashed", color="red", weight=0]; 5113[label="reduce2D (Pos (primPlusNat vuz171 vuz207)) (Neg vuz71)",fontsize=16,color="magenta"];5113 -> 5690[label="",style="dashed", color="magenta", weight=3]; 2665[label="vuz173",fontsize=16,color="green",shape="box"];2666[label="vuz71",fontsize=16,color="green",shape="box"];2667[label="vuz209",fontsize=16,color="green",shape="box"];4225 -> 678[label="",style="dashed", color="red", weight=0]; 4225[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];4225 -> 4257[label="",style="dashed", color="magenta", weight=3]; 4225 -> 4258[label="",style="dashed", color="magenta", weight=3]; 4226 -> 678[label="",style="dashed", color="red", weight=0]; 4226[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];4226 -> 4259[label="",style="dashed", color="magenta", weight=3]; 4226 -> 4260[label="",style="dashed", color="magenta", weight=3]; 4224[label="gcd2 (primEqInt (primPlusInt (Pos vuz289) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz288) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4224 -> 4261[label="",style="solid", color="black", weight=3]; 4228 -> 678[label="",style="dashed", color="red", weight=0]; 4228[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];4228 -> 4262[label="",style="dashed", color="magenta", weight=3]; 4228 -> 4263[label="",style="dashed", color="magenta", weight=3]; 4229 -> 678[label="",style="dashed", color="red", weight=0]; 4229[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];4229 -> 4264[label="",style="dashed", color="magenta", weight=3]; 4229 -> 4265[label="",style="dashed", color="magenta", weight=3]; 4227[label="gcd2 (primEqInt (primPlusInt (Neg vuz291) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz290) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4227 -> 4266[label="",style="solid", color="black", weight=3]; 2678[label="vuz175",fontsize=16,color="green",shape="box"];2679[label="vuz74",fontsize=16,color="green",shape="box"];2680[label="vuz211",fontsize=16,color="green",shape="box"];5114 -> 1352[label="",style="dashed", color="red", weight=0]; 5114[label="primPlusNat vuz177 vuz213",fontsize=16,color="magenta"];5114 -> 5703[label="",style="dashed", color="magenta", weight=3]; 5114 -> 5704[label="",style="dashed", color="magenta", weight=3]; 5115 -> 5705[label="",style="dashed", color="red", weight=0]; 5115[label="reduce2D (Pos (primPlusNat vuz177 vuz213)) (Pos vuz74)",fontsize=16,color="magenta"];5115 -> 5706[label="",style="dashed", color="magenta", weight=3]; 5831 -> 678[label="",style="dashed", color="red", weight=0]; 5831[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];5831 -> 5858[label="",style="dashed", color="magenta", weight=3]; 5831 -> 5859[label="",style="dashed", color="magenta", weight=3]; 5832 -> 678[label="",style="dashed", color="red", weight=0]; 5832[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];5832 -> 5860[label="",style="dashed", color="magenta", weight=3]; 5832 -> 5861[label="",style="dashed", color="magenta", weight=3]; 5830[label="gcd2 (primEqInt (primPlusInt (Neg vuz354) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz353) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5830 -> 5862[label="",style="solid", color="black", weight=3]; 5834 -> 678[label="",style="dashed", color="red", weight=0]; 5834[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];5834 -> 5863[label="",style="dashed", color="magenta", weight=3]; 5834 -> 5864[label="",style="dashed", color="magenta", weight=3]; 5835 -> 678[label="",style="dashed", color="red", weight=0]; 5835[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];5835 -> 5865[label="",style="dashed", color="magenta", weight=3]; 5835 -> 5866[label="",style="dashed", color="magenta", weight=3]; 5833[label="gcd2 (primEqInt (primPlusInt (Pos vuz356) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz355) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5833 -> 5867[label="",style="solid", color="black", weight=3]; 5837 -> 678[label="",style="dashed", color="red", weight=0]; 5837[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];5837 -> 5868[label="",style="dashed", color="magenta", weight=3]; 5837 -> 5869[label="",style="dashed", color="magenta", weight=3]; 5838 -> 678[label="",style="dashed", color="red", weight=0]; 5838[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];5838 -> 5870[label="",style="dashed", color="magenta", weight=3]; 5838 -> 5871[label="",style="dashed", color="magenta", weight=3]; 5836[label="gcd2 (primEqInt (primPlusInt (Pos vuz358) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz357) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="triangle"];5836 -> 5872[label="",style="solid", color="black", weight=3]; 5840 -> 678[label="",style="dashed", color="red", weight=0]; 5840[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];5840 -> 5873[label="",style="dashed", color="magenta", weight=3]; 5840 -> 5874[label="",style="dashed", color="magenta", weight=3]; 5841 -> 678[label="",style="dashed", color="red", weight=0]; 5841[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];5841 -> 5875[label="",style="dashed", color="magenta", weight=3]; 5841 -> 5876[label="",style="dashed", color="magenta", weight=3]; 5839[label="gcd2 (primEqInt (primPlusInt (Neg vuz360) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz359) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="triangle"];5839 -> 5877[label="",style="solid", color="black", weight=3]; 4231 -> 678[label="",style="dashed", color="red", weight=0]; 4231[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];4231 -> 4267[label="",style="dashed", color="magenta", weight=3]; 4231 -> 4268[label="",style="dashed", color="magenta", weight=3]; 4232 -> 678[label="",style="dashed", color="red", weight=0]; 4232[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];4232 -> 4269[label="",style="dashed", color="magenta", weight=3]; 4232 -> 4270[label="",style="dashed", color="magenta", weight=3]; 4230[label="gcd2 (primEqInt (primPlusInt (Neg vuz293) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz292) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="triangle"];4230 -> 4271[label="",style="solid", color="black", weight=3]; 4234 -> 678[label="",style="dashed", color="red", weight=0]; 4234[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];4234 -> 4272[label="",style="dashed", color="magenta", weight=3]; 4234 -> 4273[label="",style="dashed", color="magenta", weight=3]; 4235 -> 678[label="",style="dashed", color="red", weight=0]; 4235[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];4235 -> 4274[label="",style="dashed", color="magenta", weight=3]; 4235 -> 4275[label="",style="dashed", color="magenta", weight=3]; 4233[label="gcd2 (primEqInt (primPlusInt (Pos vuz295) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz294) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="triangle"];4233 -> 4276[label="",style="solid", color="black", weight=3]; 4237 -> 678[label="",style="dashed", color="red", weight=0]; 4237[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];4237 -> 4277[label="",style="dashed", color="magenta", weight=3]; 4237 -> 4278[label="",style="dashed", color="magenta", weight=3]; 4238 -> 678[label="",style="dashed", color="red", weight=0]; 4238[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];4238 -> 4279[label="",style="dashed", color="magenta", weight=3]; 4238 -> 4280[label="",style="dashed", color="magenta", weight=3]; 4236[label="gcd2 (primEqInt (primPlusInt (Pos vuz297) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz296) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="triangle"];4236 -> 4281[label="",style="solid", color="black", weight=3]; 4240 -> 678[label="",style="dashed", color="red", weight=0]; 4240[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];4240 -> 4282[label="",style="dashed", color="magenta", weight=3]; 4240 -> 4283[label="",style="dashed", color="magenta", weight=3]; 4241 -> 678[label="",style="dashed", color="red", weight=0]; 4241[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];4241 -> 4284[label="",style="dashed", color="magenta", weight=3]; 4241 -> 4285[label="",style="dashed", color="magenta", weight=3]; 4239[label="gcd2 (primEqInt (primPlusInt (Neg vuz299) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz298) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="triangle"];4239 -> 4286[label="",style="solid", color="black", weight=3]; 5843 -> 678[label="",style="dashed", color="red", weight=0]; 5843[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];5843 -> 5878[label="",style="dashed", color="magenta", weight=3]; 5843 -> 5879[label="",style="dashed", color="magenta", weight=3]; 5844 -> 678[label="",style="dashed", color="red", weight=0]; 5844[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];5844 -> 5880[label="",style="dashed", color="magenta", weight=3]; 5844 -> 5881[label="",style="dashed", color="magenta", weight=3]; 5842[label="gcd2 (primEqInt (primPlusInt (Neg vuz362) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz361) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="triangle"];5842 -> 5882[label="",style="solid", color="black", weight=3]; 5846 -> 678[label="",style="dashed", color="red", weight=0]; 5846[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];5846 -> 5883[label="",style="dashed", color="magenta", weight=3]; 5846 -> 5884[label="",style="dashed", color="magenta", weight=3]; 5847 -> 678[label="",style="dashed", color="red", weight=0]; 5847[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];5847 -> 5885[label="",style="dashed", color="magenta", weight=3]; 5847 -> 5886[label="",style="dashed", color="magenta", weight=3]; 5845[label="gcd2 (primEqInt (primPlusInt (Pos vuz364) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz363) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="triangle"];5845 -> 5887[label="",style="solid", color="black", weight=3]; 2734[label="primQuotInt (primMinusNat (Succ vuz1850) (Succ vuz1990)) (reduce2D (primMinusNat (Succ vuz1850) (Succ vuz1990)) (Pos vuz144))",fontsize=16,color="black",shape="box"];2734 -> 2778[label="",style="solid", color="black", weight=3]; 2735[label="primQuotInt (primMinusNat (Succ vuz1850) Zero) (reduce2D (primMinusNat (Succ vuz1850) Zero) (Pos vuz144))",fontsize=16,color="black",shape="box"];2735 -> 2779[label="",style="solid", color="black", weight=3]; 2736[label="primQuotInt (primMinusNat Zero (Succ vuz1990)) (reduce2D (primMinusNat Zero (Succ vuz1990)) (Pos vuz144))",fontsize=16,color="black",shape="box"];2736 -> 2780[label="",style="solid", color="black", weight=3]; 2737[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero Zero) (Pos vuz144))",fontsize=16,color="black",shape="box"];2737 -> 2781[label="",style="solid", color="black", weight=3]; 4089 -> 1352[label="",style="dashed", color="red", weight=0]; 4089[label="primPlusNat vuz187 vuz201",fontsize=16,color="magenta"];4089 -> 4114[label="",style="dashed", color="magenta", weight=3]; 4089 -> 4115[label="",style="dashed", color="magenta", weight=3]; 4088[label="reduce2D (Neg vuz282) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];4088 -> 4116[label="",style="solid", color="black", weight=3]; 4099[label="vuz201",fontsize=16,color="green",shape="box"];4100[label="vuz187",fontsize=16,color="green",shape="box"];5848[label="vuz90",fontsize=16,color="green",shape="box"];5849[label="vuz10",fontsize=16,color="green",shape="box"];5850[label="vuz90",fontsize=16,color="green",shape="box"];5851[label="vuz10",fontsize=16,color="green",shape="box"];5852[label="gcd2 (primEqInt (primPlusInt (Pos vuz350) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz349) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5852 -> 5898[label="",style="solid", color="black", weight=3]; 5853[label="vuz90",fontsize=16,color="green",shape="box"];5854[label="vuz10",fontsize=16,color="green",shape="box"];5855[label="vuz90",fontsize=16,color="green",shape="box"];5856[label="vuz10",fontsize=16,color="green",shape="box"];5857[label="gcd2 (primEqInt (primPlusInt (Neg vuz352) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz351) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5857 -> 5899[label="",style="solid", color="black", weight=3]; 4102 -> 1352[label="",style="dashed", color="red", weight=0]; 4102[label="primPlusNat vuz167 vuz203",fontsize=16,color="magenta"];4102 -> 4117[label="",style="dashed", color="magenta", weight=3]; 4102 -> 4118[label="",style="dashed", color="magenta", weight=3]; 4101[label="reduce2D (Neg vuz283) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4101 -> 4119[label="",style="solid", color="black", weight=3]; 4112[label="vuz203",fontsize=16,color="green",shape="box"];4113[label="vuz167",fontsize=16,color="green",shape="box"];2750[label="primQuotInt (primMinusNat (Succ vuz1690) (Succ vuz2050)) (reduce2D (primMinusNat (Succ vuz1690) (Succ vuz2050)) (Neg vuz68))",fontsize=16,color="black",shape="box"];2750 -> 2802[label="",style="solid", color="black", weight=3]; 2751[label="primQuotInt (primMinusNat (Succ vuz1690) Zero) (reduce2D (primMinusNat (Succ vuz1690) Zero) (Neg vuz68))",fontsize=16,color="black",shape="box"];2751 -> 2803[label="",style="solid", color="black", weight=3]; 2752[label="primQuotInt (primMinusNat Zero (Succ vuz2050)) (reduce2D (primMinusNat Zero (Succ vuz2050)) (Neg vuz68))",fontsize=16,color="black",shape="box"];2752 -> 2804[label="",style="solid", color="black", weight=3]; 2753[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero Zero) (Neg vuz68))",fontsize=16,color="black",shape="box"];2753 -> 2805[label="",style="solid", color="black", weight=3]; 4242[label="vuz200",fontsize=16,color="green",shape="box"];4243[label="vuz21",fontsize=16,color="green",shape="box"];4244[label="vuz200",fontsize=16,color="green",shape="box"];4245[label="vuz21",fontsize=16,color="green",shape="box"];4246[label="gcd2 (primEqInt (primPlusInt (Neg vuz285) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz284) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4246 -> 4295[label="",style="solid", color="black", weight=3]; 4247[label="vuz200",fontsize=16,color="green",shape="box"];4248[label="vuz21",fontsize=16,color="green",shape="box"];4249[label="vuz200",fontsize=16,color="green",shape="box"];4250[label="vuz21",fontsize=16,color="green",shape="box"];4251[label="gcd2 (primEqInt (primPlusInt (Pos vuz287) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz286) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4251 -> 4296[label="",style="solid", color="black", weight=3]; 4926[label="vuz28000",fontsize=16,color="green",shape="box"];4927[label="vuz281000",fontsize=16,color="green",shape="box"];4928[label="vuz281000",fontsize=16,color="green",shape="box"];4929[label="vuz28000",fontsize=16,color="green",shape="box"];4925[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS vuz340 vuz341)",fontsize=16,color="burlywood",shape="triangle"];6536[label="vuz340/Succ vuz3400",fontsize=10,color="white",style="solid",shape="box"];4925 -> 6536[label="",style="solid", color="burlywood", weight=9]; 6536 -> 4966[label="",style="solid", color="burlywood", weight=3]; 6537[label="vuz340/Zero",fontsize=10,color="white",style="solid",shape="box"];4925 -> 6537[label="",style="solid", color="burlywood", weight=9]; 6537 -> 4967[label="",style="solid", color="burlywood", weight=3]; 4254[label="Succ (primDivNatS (primMinusNatS (Succ vuz28000) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];4254 -> 4301[label="",style="dashed", color="green", weight=3]; 4255[label="Zero",fontsize=16,color="green",shape="box"];4256[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];4256 -> 4302[label="",style="dashed", color="green", weight=3]; 5687[label="vuz207",fontsize=16,color="green",shape="box"];5688[label="vuz171",fontsize=16,color="green",shape="box"];5690 -> 1352[label="",style="dashed", color="red", weight=0]; 5690[label="primPlusNat vuz171 vuz207",fontsize=16,color="magenta"];5690 -> 5719[label="",style="dashed", color="magenta", weight=3]; 5690 -> 5720[label="",style="dashed", color="magenta", weight=3]; 5689[label="reduce2D (Pos vuz347) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];5689 -> 5721[label="",style="solid", color="black", weight=3]; 4257[label="vuz250",fontsize=16,color="green",shape="box"];4258[label="vuz26",fontsize=16,color="green",shape="box"];4259[label="vuz250",fontsize=16,color="green",shape="box"];4260[label="vuz26",fontsize=16,color="green",shape="box"];4261[label="gcd2 (primEqInt (primPlusInt (Pos vuz289) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz288) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4261 -> 4303[label="",style="solid", color="black", weight=3]; 4262[label="vuz250",fontsize=16,color="green",shape="box"];4263[label="vuz26",fontsize=16,color="green",shape="box"];4264[label="vuz250",fontsize=16,color="green",shape="box"];4265[label="vuz26",fontsize=16,color="green",shape="box"];4266[label="gcd2 (primEqInt (primPlusInt (Neg vuz291) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz290) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4266 -> 4304[label="",style="solid", color="black", weight=3]; 5703[label="vuz213",fontsize=16,color="green",shape="box"];5704[label="vuz177",fontsize=16,color="green",shape="box"];5706 -> 1352[label="",style="dashed", color="red", weight=0]; 5706[label="primPlusNat vuz177 vuz213",fontsize=16,color="magenta"];5706 -> 5722[label="",style="dashed", color="magenta", weight=3]; 5706 -> 5723[label="",style="dashed", color="magenta", weight=3]; 5705[label="reduce2D (Pos vuz348) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5705 -> 5724[label="",style="solid", color="black", weight=3]; 5858[label="vuz300",fontsize=16,color="green",shape="box"];5859[label="vuz31",fontsize=16,color="green",shape="box"];5860[label="vuz300",fontsize=16,color="green",shape="box"];5861[label="vuz31",fontsize=16,color="green",shape="box"];5862[label="gcd2 (primEqInt (primPlusInt (Neg vuz354) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz353) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5862 -> 5900[label="",style="solid", color="black", weight=3]; 5863[label="vuz300",fontsize=16,color="green",shape="box"];5864[label="vuz31",fontsize=16,color="green",shape="box"];5865[label="vuz300",fontsize=16,color="green",shape="box"];5866[label="vuz31",fontsize=16,color="green",shape="box"];5867[label="gcd2 (primEqInt (primPlusInt (Pos vuz356) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz355) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5867 -> 5901[label="",style="solid", color="black", weight=3]; 5868[label="vuz350",fontsize=16,color="green",shape="box"];5869[label="vuz36",fontsize=16,color="green",shape="box"];5870[label="vuz350",fontsize=16,color="green",shape="box"];5871[label="vuz36",fontsize=16,color="green",shape="box"];5872[label="gcd2 (primEqInt (primPlusInt (Pos vuz358) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz357) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5872 -> 5902[label="",style="solid", color="black", weight=3]; 5873[label="vuz350",fontsize=16,color="green",shape="box"];5874[label="vuz36",fontsize=16,color="green",shape="box"];5875[label="vuz350",fontsize=16,color="green",shape="box"];5876[label="vuz36",fontsize=16,color="green",shape="box"];5877[label="gcd2 (primEqInt (primPlusInt (Neg vuz360) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz359) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5877 -> 5903[label="",style="solid", color="black", weight=3]; 4267[label="vuz400",fontsize=16,color="green",shape="box"];4268[label="vuz41",fontsize=16,color="green",shape="box"];4269[label="vuz400",fontsize=16,color="green",shape="box"];4270[label="vuz41",fontsize=16,color="green",shape="box"];4271[label="gcd2 (primEqInt (primPlusInt (Neg vuz293) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz292) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4271 -> 4305[label="",style="solid", color="black", weight=3]; 4272[label="vuz400",fontsize=16,color="green",shape="box"];4273[label="vuz41",fontsize=16,color="green",shape="box"];4274[label="vuz400",fontsize=16,color="green",shape="box"];4275[label="vuz41",fontsize=16,color="green",shape="box"];4276[label="gcd2 (primEqInt (primPlusInt (Pos vuz295) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz294) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4276 -> 4306[label="",style="solid", color="black", weight=3]; 4277[label="vuz450",fontsize=16,color="green",shape="box"];4278[label="vuz46",fontsize=16,color="green",shape="box"];4279[label="vuz450",fontsize=16,color="green",shape="box"];4280[label="vuz46",fontsize=16,color="green",shape="box"];4281[label="gcd2 (primEqInt (primPlusInt (Pos vuz297) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz296) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4281 -> 4307[label="",style="solid", color="black", weight=3]; 4282[label="vuz450",fontsize=16,color="green",shape="box"];4283[label="vuz46",fontsize=16,color="green",shape="box"];4284[label="vuz450",fontsize=16,color="green",shape="box"];4285[label="vuz46",fontsize=16,color="green",shape="box"];4286[label="gcd2 (primEqInt (primPlusInt (Neg vuz299) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz298) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4286 -> 4308[label="",style="solid", color="black", weight=3]; 5878[label="vuz500",fontsize=16,color="green",shape="box"];5879[label="vuz51",fontsize=16,color="green",shape="box"];5880[label="vuz500",fontsize=16,color="green",shape="box"];5881[label="vuz51",fontsize=16,color="green",shape="box"];5882[label="gcd2 (primEqInt (primPlusInt (Neg vuz362) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz361) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5882 -> 5904[label="",style="solid", color="black", weight=3]; 5883[label="vuz500",fontsize=16,color="green",shape="box"];5884[label="vuz51",fontsize=16,color="green",shape="box"];5885[label="vuz500",fontsize=16,color="green",shape="box"];5886[label="vuz51",fontsize=16,color="green",shape="box"];5887[label="gcd2 (primEqInt (primPlusInt (Pos vuz364) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz363) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5887 -> 5905[label="",style="solid", color="black", weight=3]; 2778 -> 2516[label="",style="dashed", color="red", weight=0]; 2778[label="primQuotInt (primMinusNat vuz1850 vuz1990) (reduce2D (primMinusNat vuz1850 vuz1990) (Pos vuz144))",fontsize=16,color="magenta"];2778 -> 2862[label="",style="dashed", color="magenta", weight=3]; 2778 -> 2863[label="",style="dashed", color="magenta", weight=3]; 2779 -> 5044[label="",style="dashed", color="red", weight=0]; 2779[label="primQuotInt (Pos (Succ vuz1850)) (reduce2D (Pos (Succ vuz1850)) (Pos vuz144))",fontsize=16,color="magenta"];2779 -> 5162[label="",style="dashed", color="magenta", weight=3]; 2779 -> 5163[label="",style="dashed", color="magenta", weight=3]; 2780 -> 3507[label="",style="dashed", color="red", weight=0]; 2780[label="primQuotInt (Neg (Succ vuz1990)) (reduce2D (Neg (Succ vuz1990)) (Pos vuz144))",fontsize=16,color="magenta"];2780 -> 3640[label="",style="dashed", color="magenta", weight=3]; 2780 -> 3641[label="",style="dashed", color="magenta", weight=3]; 2781 -> 5044[label="",style="dashed", color="red", weight=0]; 2781[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos vuz144))",fontsize=16,color="magenta"];2781 -> 5164[label="",style="dashed", color="magenta", weight=3]; 2781 -> 5165[label="",style="dashed", color="magenta", weight=3]; 4114[label="vuz201",fontsize=16,color="green",shape="box"];4115[label="vuz187",fontsize=16,color="green",shape="box"];4116[label="gcd (Neg vuz282) (Pos vuz144)",fontsize=16,color="black",shape="box"];4116 -> 4133[label="",style="solid", color="black", weight=3]; 5898 -> 5918[label="",style="dashed", color="red", weight=0]; 5898[label="gcd2 (primEqInt (primPlusInt (Pos vuz350) (Neg (primMulNat vuz11 (Succ vuz12)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz349) (Neg (primMulNat vuz11 (Succ vuz12)))) (Pos vuz144)",fontsize=16,color="magenta"];5898 -> 5919[label="",style="dashed", color="magenta", weight=3]; 5898 -> 5920[label="",style="dashed", color="magenta", weight=3]; 5899 -> 5926[label="",style="dashed", color="red", weight=0]; 5899[label="gcd2 (primEqInt (primPlusInt (Neg vuz352) (Neg (primMulNat vuz11 (Succ vuz12)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz351) (Neg (primMulNat vuz11 (Succ vuz12)))) (Pos vuz144)",fontsize=16,color="magenta"];5899 -> 5927[label="",style="dashed", color="magenta", weight=3]; 5899 -> 5928[label="",style="dashed", color="magenta", weight=3]; 4117[label="vuz203",fontsize=16,color="green",shape="box"];4118[label="vuz167",fontsize=16,color="green",shape="box"];4119[label="gcd (Neg vuz283) (Neg vuz68)",fontsize=16,color="black",shape="box"];4119 -> 4134[label="",style="solid", color="black", weight=3]; 2802 -> 2537[label="",style="dashed", color="red", weight=0]; 2802[label="primQuotInt (primMinusNat vuz1690 vuz2050) (reduce2D (primMinusNat vuz1690 vuz2050) (Neg vuz68))",fontsize=16,color="magenta"];2802 -> 2884[label="",style="dashed", color="magenta", weight=3]; 2802 -> 2885[label="",style="dashed", color="magenta", weight=3]; 2803 -> 5044[label="",style="dashed", color="red", weight=0]; 2803[label="primQuotInt (Pos (Succ vuz1690)) (reduce2D (Pos (Succ vuz1690)) (Neg vuz68))",fontsize=16,color="magenta"];2803 -> 5170[label="",style="dashed", color="magenta", weight=3]; 2803 -> 5171[label="",style="dashed", color="magenta", weight=3]; 2804 -> 3507[label="",style="dashed", color="red", weight=0]; 2804[label="primQuotInt (Neg (Succ vuz2050)) (reduce2D (Neg (Succ vuz2050)) (Neg vuz68))",fontsize=16,color="magenta"];2804 -> 3646[label="",style="dashed", color="magenta", weight=3]; 2804 -> 3647[label="",style="dashed", color="magenta", weight=3]; 2805 -> 5044[label="",style="dashed", color="red", weight=0]; 2805[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg vuz68))",fontsize=16,color="magenta"];2805 -> 5172[label="",style="dashed", color="magenta", weight=3]; 2805 -> 5173[label="",style="dashed", color="magenta", weight=3]; 4295 -> 4317[label="",style="dashed", color="red", weight=0]; 4295[label="gcd2 (primEqInt (primPlusInt (Neg vuz285) (Neg (primMulNat vuz22 (Succ vuz23)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz284) (Neg (primMulNat vuz22 (Succ vuz23)))) (Neg vuz68)",fontsize=16,color="magenta"];4295 -> 4318[label="",style="dashed", color="magenta", weight=3]; 4295 -> 4319[label="",style="dashed", color="magenta", weight=3]; 4296 -> 4325[label="",style="dashed", color="red", weight=0]; 4296[label="gcd2 (primEqInt (primPlusInt (Pos vuz287) (Neg (primMulNat vuz22 (Succ vuz23)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz286) (Neg (primMulNat vuz22 (Succ vuz23)))) (Neg vuz68)",fontsize=16,color="magenta"];4296 -> 4326[label="",style="dashed", color="magenta", weight=3]; 4296 -> 4327[label="",style="dashed", color="magenta", weight=3]; 4966[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS (Succ vuz3400) vuz341)",fontsize=16,color="burlywood",shape="box"];6538[label="vuz341/Succ 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color="red", weight=0]; 4301[label="primDivNatS (primMinusNatS (Succ vuz28000) Zero) (Succ Zero)",fontsize=16,color="magenta"];4301 -> 4337[label="",style="dashed", color="magenta", weight=3]; 4301 -> 4338[label="",style="dashed", color="magenta", weight=3]; 4302 -> 4127[label="",style="dashed", color="red", weight=0]; 4302[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];4302 -> 4339[label="",style="dashed", color="magenta", weight=3]; 4302 -> 4340[label="",style="dashed", color="magenta", weight=3]; 5719[label="vuz207",fontsize=16,color="green",shape="box"];5720[label="vuz171",fontsize=16,color="green",shape="box"];5721[label="gcd (Pos vuz347) (Neg vuz71)",fontsize=16,color="black",shape="box"];5721 -> 5739[label="",style="solid", color="black", weight=3]; 4303 -> 4341[label="",style="dashed", color="red", weight=0]; 4303[label="gcd2 (primEqInt (primPlusInt (Pos vuz289) (Pos (primMulNat vuz27 (Succ vuz28)))) (fromInt (Pos Zero))) (primPlusInt 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(primPlusInt (Neg vuz354) (Pos (primMulNat vuz32 (Succ vuz33)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz353) (Pos (primMulNat vuz32 (Succ vuz33)))) (Pos vuz74)",fontsize=16,color="magenta"];5900 -> 5935[label="",style="dashed", color="magenta", weight=3]; 5900 -> 5936[label="",style="dashed", color="magenta", weight=3]; 5901 -> 5942[label="",style="dashed", color="red", weight=0]; 5901[label="gcd2 (primEqInt (primPlusInt (Pos vuz356) (Pos (primMulNat vuz32 (Succ vuz33)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz355) (Pos (primMulNat vuz32 (Succ vuz33)))) (Pos vuz74)",fontsize=16,color="magenta"];5901 -> 5943[label="",style="dashed", color="magenta", weight=3]; 5901 -> 5944[label="",style="dashed", color="magenta", weight=3]; 5902 -> 5942[label="",style="dashed", color="red", weight=0]; 5902[label="gcd2 (primEqInt (primPlusInt (Pos vuz358) (Pos (primMulNat vuz37 (Succ vuz38)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz357) (Pos (primMulNat vuz37 (Succ vuz38)))) (Pos 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4349[label="",style="dashed", color="red", weight=0]; 4305[label="gcd2 (primEqInt (primPlusInt (Neg vuz293) (Pos (primMulNat vuz42 (Succ vuz43)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz292) (Pos (primMulNat vuz42 (Succ vuz43)))) (Neg vuz92)",fontsize=16,color="magenta"];4305 -> 4352[label="",style="dashed", color="magenta", weight=3]; 4305 -> 4353[label="",style="dashed", color="magenta", weight=3]; 4305 -> 4354[label="",style="dashed", color="magenta", weight=3]; 4305 -> 4355[label="",style="dashed", color="magenta", weight=3]; 4305 -> 4356[label="",style="dashed", color="magenta", weight=3]; 4306 -> 4341[label="",style="dashed", color="red", weight=0]; 4306[label="gcd2 (primEqInt (primPlusInt (Pos vuz295) (Pos (primMulNat vuz42 (Succ vuz43)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz294) (Pos (primMulNat vuz42 (Succ vuz43)))) (Neg vuz92)",fontsize=16,color="magenta"];4306 -> 4344[label="",style="dashed", color="magenta", weight=3]; 4306 -> 4345[label="",style="dashed", color="magenta", weight=3]; 4306 -> 4346[label="",style="dashed", color="magenta", weight=3]; 4306 -> 4347[label="",style="dashed", color="magenta", weight=3]; 4306 -> 4348[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4325[label="",style="dashed", color="red", weight=0]; 4307[label="gcd2 (primEqInt (primPlusInt (Pos vuz297) (Neg (primMulNat vuz47 (Succ vuz48)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz296) (Neg (primMulNat vuz47 (Succ vuz48)))) (Neg vuz107)",fontsize=16,color="magenta"];4307 -> 4328[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4329[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4330[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4331[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4332[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4317[label="",style="dashed", color="red", weight=0]; 4308[label="gcd2 (primEqInt (primPlusInt (Neg vuz299) (Neg (primMulNat vuz47 (Succ vuz48)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz298) (Neg (primMulNat vuz47 (Succ vuz48)))) (Neg vuz107)",fontsize=16,color="magenta"];4308 -> 4320[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4321[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4322[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4323[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4324[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5926[label="",style="dashed", color="red", weight=0]; 5904[label="gcd2 (primEqInt (primPlusInt (Neg vuz362) (Neg (primMulNat vuz52 (Succ vuz53)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz361) (Neg (primMulNat vuz52 (Succ vuz53)))) (Pos vuz122)",fontsize=16,color="magenta"];5904 -> 5929[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5930[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5931[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5932[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5933[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5918[label="",style="dashed", color="red", weight=0]; 5905[label="gcd2 (primEqInt (primPlusInt (Pos vuz364) (Neg (primMulNat vuz52 (Succ vuz53)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz363) (Neg (primMulNat vuz52 (Succ vuz53)))) (Pos vuz122)",fontsize=16,color="magenta"];5905 -> 5921[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5922[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5923[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5924[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5925[label="",style="dashed", color="magenta", weight=3]; 2862[label="vuz1990",fontsize=16,color="green",shape="box"];2863[label="vuz1850",fontsize=16,color="green",shape="box"];5162[label="Succ vuz1850",fontsize=16,color="green",shape="box"];5163 -> 5705[label="",style="dashed", color="red", weight=0]; 5163[label="reduce2D (Pos (Succ vuz1850)) (Pos vuz144)",fontsize=16,color="magenta"];5163 -> 5707[label="",style="dashed", color="magenta", weight=3]; 5163 -> 5708[label="",style="dashed", color="magenta", weight=3]; 3640 -> 4088[label="",style="dashed", color="red", weight=0]; 3640[label="reduce2D (Neg (Succ vuz1990)) (Pos vuz144)",fontsize=16,color="magenta"];3640 -> 4090[label="",style="dashed", color="magenta", weight=3]; 3641[label="Succ vuz1990",fontsize=16,color="green",shape="box"];5164[label="Zero",fontsize=16,color="green",shape="box"];5165 -> 5705[label="",style="dashed", color="red", weight=0]; 5165[label="reduce2D (Pos Zero) (Pos vuz144)",fontsize=16,color="magenta"];5165 -> 5709[label="",style="dashed", color="magenta", weight=3]; 5165 -> 5710[label="",style="dashed", color="magenta", weight=3]; 4133[label="gcd3 (Neg vuz282) (Pos vuz144)",fontsize=16,color="black",shape="box"];4133 -> 4149[label="",style="solid", color="black", weight=3]; 5919 -> 678[label="",style="dashed", color="red", weight=0]; 5919[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];5919 -> 5950[label="",style="dashed", color="magenta", weight=3]; 5919 -> 5951[label="",style="dashed", color="magenta", weight=3]; 5920 -> 678[label="",style="dashed", color="red", weight=0]; 5920[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];5920 -> 5952[label="",style="dashed", color="magenta", weight=3]; 5920 -> 5953[label="",style="dashed", color="magenta", weight=3]; 5918[label="gcd2 (primEqInt (primPlusInt (Pos vuz350) (Neg vuz366)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz349) (Neg vuz365)) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];5918 -> 5954[label="",style="solid", color="black", weight=3]; 5927 -> 678[label="",style="dashed", color="red", weight=0]; 5927[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];5927 -> 5955[label="",style="dashed", color="magenta", weight=3]; 5927 -> 5956[label="",style="dashed", color="magenta", weight=3]; 5928 -> 678[label="",style="dashed", color="red", weight=0]; 5928[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];5928 -> 5957[label="",style="dashed", color="magenta", weight=3]; 5928 -> 5958[label="",style="dashed", color="magenta", weight=3]; 5926[label="gcd2 (primEqInt (primPlusInt (Neg vuz352) (Neg vuz368)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz351) (Neg vuz367)) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];5926 -> 5959[label="",style="solid", color="black", weight=3]; 4134[label="gcd3 (Neg vuz283) (Neg vuz68)",fontsize=16,color="black",shape="box"];4134 -> 4150[label="",style="solid", color="black", weight=3]; 2884[label="vuz2050",fontsize=16,color="green",shape="box"];2885[label="vuz1690",fontsize=16,color="green",shape="box"];5170[label="Succ vuz1690",fontsize=16,color="green",shape="box"];5171 -> 5689[label="",style="dashed", color="red", weight=0]; 5171[label="reduce2D (Pos (Succ vuz1690)) (Neg vuz68)",fontsize=16,color="magenta"];5171 -> 5691[label="",style="dashed", color="magenta", weight=3]; 5171 -> 5692[label="",style="dashed", color="magenta", weight=3]; 3646 -> 4101[label="",style="dashed", color="red", weight=0]; 3646[label="reduce2D (Neg (Succ vuz2050)) (Neg vuz68)",fontsize=16,color="magenta"];3646 -> 4103[label="",style="dashed", color="magenta", weight=3]; 3647[label="Succ vuz2050",fontsize=16,color="green",shape="box"];5172[label="Zero",fontsize=16,color="green",shape="box"];5173 -> 5689[label="",style="dashed", color="red", weight=0]; 5173[label="reduce2D (Pos Zero) (Neg vuz68)",fontsize=16,color="magenta"];5173 -> 5693[label="",style="dashed", color="magenta", weight=3]; 5173 -> 5694[label="",style="dashed", color="magenta", weight=3]; 4318 -> 678[label="",style="dashed", color="red", weight=0]; 4318[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];4318 -> 4357[label="",style="dashed", color="magenta", weight=3]; 4318 -> 4358[label="",style="dashed", color="magenta", weight=3]; 4319 -> 678[label="",style="dashed", color="red", weight=0]; 4319[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];4319 -> 4359[label="",style="dashed", color="magenta", weight=3]; 4319 -> 4360[label="",style="dashed", color="magenta", weight=3]; 4317[label="gcd2 (primEqInt (primPlusInt (Neg vuz285) (Neg vuz301)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz284) (Neg vuz300)) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4317 -> 4361[label="",style="solid", color="black", weight=3]; 4326 -> 678[label="",style="dashed", color="red", weight=0]; 4326[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];4326 -> 4362[label="",style="dashed", color="magenta", weight=3]; 4326 -> 4363[label="",style="dashed", color="magenta", weight=3]; 4327 -> 678[label="",style="dashed", color="red", weight=0]; 4327[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];4327 -> 4364[label="",style="dashed", color="magenta", weight=3]; 4327 -> 4365[label="",style="dashed", color="magenta", weight=3]; 4325[label="gcd2 (primEqInt (primPlusInt (Pos vuz287) (Neg vuz303)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz286) (Neg vuz302)) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4325 -> 4366[label="",style="solid", color="black", weight=3]; 4990[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS (Succ vuz3400) (Succ vuz3410))",fontsize=16,color="black",shape="box"];4990 -> 5001[label="",style="solid", color="black", weight=3]; 4991[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS (Succ vuz3400) Zero)",fontsize=16,color="black",shape="box"];4991 -> 5002[label="",style="solid", color="black", weight=3]; 4992[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS Zero (Succ vuz3410))",fontsize=16,color="black",shape="box"];4992 -> 5003[label="",style="solid", color="black", weight=3]; 4993[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];4993 -> 5004[label="",style="solid", color="black", weight=3]; 4337[label="Zero",fontsize=16,color="green",shape="box"];4338[label="primMinusNatS (Succ vuz28000) Zero",fontsize=16,color="black",shape="triangle"];4338 -> 4372[label="",style="solid", color="black", weight=3]; 4339[label="Zero",fontsize=16,color="green",shape="box"];4340[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="triangle"];4340 -> 4373[label="",style="solid", color="black", weight=3]; 5739[label="gcd3 (Pos vuz347) (Neg vuz71)",fontsize=16,color="black",shape="box"];5739 -> 5756[label="",style="solid", color="black", weight=3]; 4342 -> 678[label="",style="dashed", color="red", weight=0]; 4342[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];4342 -> 4374[label="",style="dashed", color="magenta", weight=3]; 4342 -> 4375[label="",style="dashed", color="magenta", weight=3]; 4343 -> 678[label="",style="dashed", color="red", weight=0]; 4343[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];4343 -> 4376[label="",style="dashed", color="magenta", weight=3]; 4343 -> 4377[label="",style="dashed", color="magenta", weight=3]; 4341[label="gcd2 (primEqInt (primPlusInt (Pos vuz289) (Pos vuz305)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz288) (Pos vuz304)) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4341 -> 4378[label="",style="solid", color="black", weight=3]; 4350 -> 678[label="",style="dashed", color="red", weight=0]; 4350[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];4350 -> 4379[label="",style="dashed", color="magenta", weight=3]; 4350 -> 4380[label="",style="dashed", color="magenta", weight=3]; 4351 -> 678[label="",style="dashed", color="red", weight=0]; 4351[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];4351 -> 4381[label="",style="dashed", color="magenta", weight=3]; 4351 -> 4382[label="",style="dashed", color="magenta", weight=3]; 4349[label="gcd2 (primEqInt (primPlusInt (Neg vuz291) (Pos vuz307)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz290) (Pos vuz306)) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4349 -> 4383[label="",style="solid", color="black", weight=3]; 5740[label="gcd3 (Pos vuz348) (Pos vuz74)",fontsize=16,color="black",shape="box"];5740 -> 5757[label="",style="solid", color="black", weight=3]; 5935 -> 678[label="",style="dashed", color="red", weight=0]; 5935[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];5935 -> 5960[label="",style="dashed", color="magenta", weight=3]; 5935 -> 5961[label="",style="dashed", color="magenta", weight=3]; 5936 -> 678[label="",style="dashed", color="red", weight=0]; 5936[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];5936 -> 5962[label="",style="dashed", color="magenta", weight=3]; 5936 -> 5963[label="",style="dashed", color="magenta", weight=3]; 5934[label="gcd2 (primEqInt (primPlusInt (Neg vuz354) (Pos vuz370)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz353) (Pos vuz369)) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5934 -> 5964[label="",style="solid", color="black", weight=3]; 5943 -> 678[label="",style="dashed", color="red", weight=0]; 5943[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];5943 -> 5965[label="",style="dashed", color="magenta", weight=3]; 5943 -> 5966[label="",style="dashed", color="magenta", weight=3]; 5944 -> 678[label="",style="dashed", color="red", weight=0]; 5944[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];5944 -> 5967[label="",style="dashed", color="magenta", weight=3]; 5944 -> 5968[label="",style="dashed", color="magenta", weight=3]; 5942[label="gcd2 (primEqInt (primPlusInt (Pos vuz356) (Pos vuz372)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz355) (Pos vuz371)) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5942 -> 5969[label="",style="solid", color="black", weight=3]; 5945[label="vuz357",fontsize=16,color="green",shape="box"];5946[label="vuz358",fontsize=16,color="green",shape="box"];5947 -> 678[label="",style="dashed", color="red", weight=0]; 5947[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];5947 -> 5970[label="",style="dashed", color="magenta", weight=3]; 5947 -> 5971[label="",style="dashed", color="magenta", weight=3]; 5948[label="vuz77",fontsize=16,color="green",shape="box"];5949 -> 678[label="",style="dashed", color="red", weight=0]; 5949[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];5949 -> 5972[label="",style="dashed", color="magenta", weight=3]; 5949 -> 5973[label="",style="dashed", color="magenta", weight=3]; 5937[label="vuz77",fontsize=16,color="green",shape="box"];5938[label="vuz360",fontsize=16,color="green",shape="box"];5939 -> 678[label="",style="dashed", color="red", weight=0]; 5939[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];5939 -> 5974[label="",style="dashed", color="magenta", weight=3]; 5939 -> 5975[label="",style="dashed", color="magenta", weight=3]; 5940[label="vuz359",fontsize=16,color="green",shape="box"];5941 -> 678[label="",style="dashed", color="red", weight=0]; 5941[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];5941 -> 5976[label="",style="dashed", color="magenta", weight=3]; 5941 -> 5977[label="",style="dashed", color="magenta", weight=3]; 4352[label="vuz292",fontsize=16,color="green",shape="box"];4353 -> 678[label="",style="dashed", color="red", weight=0]; 4353[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];4353 -> 4384[label="",style="dashed", color="magenta", weight=3]; 4353 -> 4385[label="",style="dashed", color="magenta", weight=3]; 4354[label="vuz92",fontsize=16,color="green",shape="box"];4355[label="vuz293",fontsize=16,color="green",shape="box"];4356 -> 678[label="",style="dashed", color="red", weight=0]; 4356[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];4356 -> 4386[label="",style="dashed", color="magenta", weight=3]; 4356 -> 4387[label="",style="dashed", color="magenta", weight=3]; 4344[label="vuz295",fontsize=16,color="green",shape="box"];4345[label="vuz92",fontsize=16,color="green",shape="box"];4346[label="vuz294",fontsize=16,color="green",shape="box"];4347 -> 678[label="",style="dashed", color="red", weight=0]; 4347[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];4347 -> 4388[label="",style="dashed", color="magenta", weight=3]; 4347 -> 4389[label="",style="dashed", color="magenta", weight=3]; 4348 -> 678[label="",style="dashed", color="red", weight=0]; 4348[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];4348 -> 4390[label="",style="dashed", color="magenta", weight=3]; 4348 -> 4391[label="",style="dashed", color="magenta", weight=3]; 4328[label="vuz296",fontsize=16,color="green",shape="box"];4329 -> 678[label="",style="dashed", color="red", weight=0]; 4329[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];4329 -> 4392[label="",style="dashed", color="magenta", weight=3]; 4329 -> 4393[label="",style="dashed", color="magenta", weight=3]; 4330[label="vuz297",fontsize=16,color="green",shape="box"];4331 -> 678[label="",style="dashed", color="red", weight=0]; 4331[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];4331 -> 4394[label="",style="dashed", color="magenta", weight=3]; 4331 -> 4395[label="",style="dashed", color="magenta", weight=3]; 4332[label="vuz107",fontsize=16,color="green",shape="box"];4320 -> 678[label="",style="dashed", color="red", weight=0]; 4320[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];4320 -> 4396[label="",style="dashed", color="magenta", weight=3]; 4320 -> 4397[label="",style="dashed", color="magenta", weight=3]; 4321[label="vuz299",fontsize=16,color="green",shape="box"];4322[label="vuz107",fontsize=16,color="green",shape="box"];4323[label="vuz298",fontsize=16,color="green",shape="box"];4324 -> 678[label="",style="dashed", color="red", weight=0]; 4324[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];4324 -> 4398[label="",style="dashed", color="magenta", weight=3]; 4324 -> 4399[label="",style="dashed", color="magenta", weight=3]; 5929 -> 678[label="",style="dashed", color="red", weight=0]; 5929[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];5929 -> 5978[label="",style="dashed", color="magenta", weight=3]; 5929 -> 5979[label="",style="dashed", color="magenta", weight=3]; 5930[label="vuz361",fontsize=16,color="green",shape="box"];5931[label="vuz122",fontsize=16,color="green",shape="box"];5932[label="vuz362",fontsize=16,color="green",shape="box"];5933 -> 678[label="",style="dashed", color="red", weight=0]; 5933[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];5933 -> 5980[label="",style="dashed", color="magenta", weight=3]; 5933 -> 5981[label="",style="dashed", color="magenta", weight=3]; 5921 -> 678[label="",style="dashed", color="red", weight=0]; 5921[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];5921 -> 5982[label="",style="dashed", color="magenta", weight=3]; 5921 -> 5983[label="",style="dashed", color="magenta", weight=3]; 5922[label="vuz363",fontsize=16,color="green",shape="box"];5923 -> 678[label="",style="dashed", color="red", weight=0]; 5923[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];5923 -> 5984[label="",style="dashed", color="magenta", weight=3]; 5923 -> 5985[label="",style="dashed", color="magenta", weight=3]; 5924[label="vuz122",fontsize=16,color="green",shape="box"];5925[label="vuz364",fontsize=16,color="green",shape="box"];5707[label="vuz144",fontsize=16,color="green",shape="box"];5708[label="Succ vuz1850",fontsize=16,color="green",shape="box"];4090[label="Succ vuz1990",fontsize=16,color="green",shape="box"];5709[label="vuz144",fontsize=16,color="green",shape="box"];5710[label="Zero",fontsize=16,color="green",shape="box"];4149[label="gcd2 (Neg vuz282 == fromInt (Pos Zero)) (Neg vuz282) (Pos vuz144)",fontsize=16,color="black",shape="box"];4149 -> 4164[label="",style="solid", color="black", weight=3]; 5950[label="vuz11",fontsize=16,color="green",shape="box"];5951[label="vuz12",fontsize=16,color="green",shape="box"];5952[label="vuz11",fontsize=16,color="green",shape="box"];5953[label="vuz12",fontsize=16,color="green",shape="box"];5954[label="gcd2 (primEqInt (primMinusNat vuz350 vuz366) (fromInt (Pos Zero))) (primMinusNat vuz350 vuz366) (Pos vuz144)",fontsize=16,color="burlywood",shape="triangle"];6542[label="vuz350/Succ vuz3500",fontsize=10,color="white",style="solid",shape="box"];5954 -> 6542[label="",style="solid", color="burlywood", weight=9]; 6542 -> 6002[label="",style="solid", color="burlywood", weight=3]; 6543[label="vuz350/Zero",fontsize=10,color="white",style="solid",shape="box"];5954 -> 6543[label="",style="solid", color="burlywood", weight=9]; 6543 -> 6003[label="",style="solid", color="burlywood", weight=3]; 5955[label="vuz11",fontsize=16,color="green",shape="box"];5956[label="vuz12",fontsize=16,color="green",shape="box"];5957[label="vuz11",fontsize=16,color="green",shape="box"];5958[label="vuz12",fontsize=16,color="green",shape="box"];5959 -> 4164[label="",style="dashed", color="red", weight=0]; 5959[label="gcd2 (primEqInt (Neg (primPlusNat vuz352 vuz368)) (fromInt (Pos Zero))) (Neg (primPlusNat vuz352 vuz368)) (Pos vuz144)",fontsize=16,color="magenta"];5959 -> 6004[label="",style="dashed", color="magenta", weight=3]; 4150[label="gcd2 (Neg vuz283 == fromInt (Pos Zero)) (Neg vuz283) (Neg vuz68)",fontsize=16,color="black",shape="box"];4150 -> 4165[label="",style="solid", color="black", weight=3]; 5691[label="vuz68",fontsize=16,color="green",shape="box"];5692[label="Succ vuz1690",fontsize=16,color="green",shape="box"];4103[label="Succ vuz2050",fontsize=16,color="green",shape="box"];5693[label="vuz68",fontsize=16,color="green",shape="box"];5694[label="Zero",fontsize=16,color="green",shape="box"];4357[label="vuz22",fontsize=16,color="green",shape="box"];4358[label="vuz23",fontsize=16,color="green",shape="box"];4359[label="vuz22",fontsize=16,color="green",shape="box"];4360[label="vuz23",fontsize=16,color="green",shape="box"];4361 -> 4165[label="",style="dashed", color="red", weight=0]; 4361[label="gcd2 (primEqInt (Neg (primPlusNat vuz285 vuz301)) (fromInt (Pos Zero))) (Neg (primPlusNat vuz285 vuz301)) (Neg vuz68)",fontsize=16,color="magenta"];4361 -> 4408[label="",style="dashed", color="magenta", weight=3]; 4362[label="vuz22",fontsize=16,color="green",shape="box"];4363[label="vuz23",fontsize=16,color="green",shape="box"];4364[label="vuz22",fontsize=16,color="green",shape="box"];4365[label="vuz23",fontsize=16,color="green",shape="box"];4366[label="gcd2 (primEqInt (primMinusNat vuz287 vuz303) (fromInt (Pos Zero))) (primMinusNat vuz287 vuz303) (Neg vuz68)",fontsize=16,color="burlywood",shape="triangle"];6544[label="vuz287/Succ vuz2870",fontsize=10,color="white",style="solid",shape="box"];4366 -> 6544[label="",style="solid", color="burlywood", weight=9]; 6544 -> 4409[label="",style="solid", color="burlywood", weight=3]; 6545[label="vuz287/Zero",fontsize=10,color="white",style="solid",shape="box"];4366 -> 6545[label="",style="solid", color="burlywood", weight=9]; 6545 -> 4410[label="",style="solid", color="burlywood", weight=3]; 5001 -> 4925[label="",style="dashed", color="red", weight=0]; 5001[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS vuz3400 vuz3410)",fontsize=16,color="magenta"];5001 -> 5011[label="",style="dashed", color="magenta", weight=3]; 5001 -> 5012[label="",style="dashed", color="magenta", weight=3]; 5002[label="primDivNatS0 (Succ vuz338) (Succ vuz339) True",fontsize=16,color="black",shape="triangle"];5002 -> 5013[label="",style="solid", color="black", weight=3]; 5003[label="primDivNatS0 (Succ vuz338) (Succ vuz339) False",fontsize=16,color="black",shape="box"];5003 -> 5014[label="",style="solid", color="black", weight=3]; 5004 -> 5002[label="",style="dashed", color="red", weight=0]; 5004[label="primDivNatS0 (Succ vuz338) (Succ vuz339) True",fontsize=16,color="magenta"];4372[label="Succ vuz28000",fontsize=16,color="green",shape="box"];4373[label="Zero",fontsize=16,color="green",shape="box"];5756[label="gcd2 (Pos vuz347 == fromInt (Pos Zero)) (Pos vuz347) (Neg vuz71)",fontsize=16,color="black",shape="box"];5756 -> 5771[label="",style="solid", color="black", weight=3]; 4374[label="vuz27",fontsize=16,color="green",shape="box"];4375[label="vuz28",fontsize=16,color="green",shape="box"];4376[label="vuz27",fontsize=16,color="green",shape="box"];4377[label="vuz28",fontsize=16,color="green",shape="box"];4378 -> 4417[label="",style="dashed", color="red", weight=0]; 4378[label="gcd2 (primEqInt (Pos (primPlusNat vuz289 vuz305)) (fromInt (Pos Zero))) (Pos (primPlusNat vuz289 vuz305)) (Neg vuz71)",fontsize=16,color="magenta"];4378 -> 4418[label="",style="dashed", color="magenta", weight=3]; 4378 -> 4419[label="",style="dashed", color="magenta", weight=3]; 4379[label="vuz27",fontsize=16,color="green",shape="box"];4380[label="vuz28",fontsize=16,color="green",shape="box"];4381[label="vuz27",fontsize=16,color="green",shape="box"];4382[label="vuz28",fontsize=16,color="green",shape="box"];4383 -> 4366[label="",style="dashed", color="red", weight=0]; 4383[label="gcd2 (primEqInt (primMinusNat vuz307 vuz291) (fromInt (Pos Zero))) (primMinusNat vuz307 vuz291) (Neg vuz71)",fontsize=16,color="magenta"];4383 -> 4420[label="",style="dashed", color="magenta", weight=3]; 4383 -> 4421[label="",style="dashed", color="magenta", weight=3]; 4383 -> 4422[label="",style="dashed", color="magenta", weight=3]; 5757[label="gcd2 (Pos vuz348 == fromInt (Pos Zero)) (Pos vuz348) (Pos vuz74)",fontsize=16,color="black",shape="box"];5757 -> 5772[label="",style="solid", color="black", weight=3]; 5960[label="vuz32",fontsize=16,color="green",shape="box"];5961[label="vuz33",fontsize=16,color="green",shape="box"];5962[label="vuz32",fontsize=16,color="green",shape="box"];5963[label="vuz33",fontsize=16,color="green",shape="box"];5964 -> 5954[label="",style="dashed", color="red", weight=0]; 5964[label="gcd2 (primEqInt (primMinusNat vuz370 vuz354) (fromInt (Pos Zero))) (primMinusNat vuz370 vuz354) (Pos vuz74)",fontsize=16,color="magenta"];5964 -> 6005[label="",style="dashed", color="magenta", weight=3]; 5964 -> 6006[label="",style="dashed", color="magenta", weight=3]; 5964 -> 6007[label="",style="dashed", color="magenta", weight=3]; 5965[label="vuz32",fontsize=16,color="green",shape="box"];5966[label="vuz33",fontsize=16,color="green",shape="box"];5967[label="vuz32",fontsize=16,color="green",shape="box"];5968[label="vuz33",fontsize=16,color="green",shape="box"];5969 -> 5772[label="",style="dashed", color="red", weight=0]; 5969[label="gcd2 (primEqInt (Pos (primPlusNat vuz356 vuz372)) (fromInt (Pos Zero))) (Pos (primPlusNat vuz356 vuz372)) (Pos vuz74)",fontsize=16,color="magenta"];5969 -> 6008[label="",style="dashed", color="magenta", weight=3]; 5970[label="vuz37",fontsize=16,color="green",shape="box"];5971[label="vuz38",fontsize=16,color="green",shape="box"];5972[label="vuz37",fontsize=16,color="green",shape="box"];5973[label="vuz38",fontsize=16,color="green",shape="box"];5974[label="vuz37",fontsize=16,color="green",shape="box"];5975[label="vuz38",fontsize=16,color="green",shape="box"];5976[label="vuz37",fontsize=16,color="green",shape="box"];5977[label="vuz38",fontsize=16,color="green",shape="box"];4384[label="vuz42",fontsize=16,color="green",shape="box"];4385[label="vuz43",fontsize=16,color="green",shape="box"];4386[label="vuz42",fontsize=16,color="green",shape="box"];4387[label="vuz43",fontsize=16,color="green",shape="box"];4388[label="vuz42",fontsize=16,color="green",shape="box"];4389[label="vuz43",fontsize=16,color="green",shape="box"];4390[label="vuz42",fontsize=16,color="green",shape="box"];4391[label="vuz43",fontsize=16,color="green",shape="box"];4392[label="vuz47",fontsize=16,color="green",shape="box"];4393[label="vuz48",fontsize=16,color="green",shape="box"];4394[label="vuz47",fontsize=16,color="green",shape="box"];4395[label="vuz48",fontsize=16,color="green",shape="box"];4396[label="vuz47",fontsize=16,color="green",shape="box"];4397[label="vuz48",fontsize=16,color="green",shape="box"];4398[label="vuz47",fontsize=16,color="green",shape="box"];4399[label="vuz48",fontsize=16,color="green",shape="box"];5978[label="vuz52",fontsize=16,color="green",shape="box"];5979[label="vuz53",fontsize=16,color="green",shape="box"];5980[label="vuz52",fontsize=16,color="green",shape="box"];5981[label="vuz53",fontsize=16,color="green",shape="box"];5982[label="vuz52",fontsize=16,color="green",shape="box"];5983[label="vuz53",fontsize=16,color="green",shape="box"];5984[label="vuz52",fontsize=16,color="green",shape="box"];5985[label="vuz53",fontsize=16,color="green",shape="box"];4164[label="gcd2 (primEqInt (Neg vuz282) (fromInt (Pos Zero))) (Neg vuz282) (Pos vuz144)",fontsize=16,color="burlywood",shape="triangle"];6546[label="vuz282/Succ vuz2820",fontsize=10,color="white",style="solid",shape="box"];4164 -> 6546[label="",style="solid", color="burlywood", weight=9]; 6546 -> 4183[label="",style="solid", color="burlywood", weight=3]; 6547[label="vuz282/Zero",fontsize=10,color="white",style="solid",shape="box"];4164 -> 6547[label="",style="solid", color="burlywood", weight=9]; 6547 -> 4184[label="",style="solid", color="burlywood", weight=3]; 6002[label="gcd2 (primEqInt (primMinusNat (Succ vuz3500) vuz366) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3500) vuz366) (Pos vuz144)",fontsize=16,color="burlywood",shape="box"];6548[label="vuz366/Succ vuz3660",fontsize=10,color="white",style="solid",shape="box"];6002 -> 6548[label="",style="solid", color="burlywood", weight=9]; 6548 -> 6024[label="",style="solid", color="burlywood", weight=3]; 6549[label="vuz366/Zero",fontsize=10,color="white",style="solid",shape="box"];6002 -> 6549[label="",style="solid", color="burlywood", weight=9]; 6549 -> 6025[label="",style="solid", color="burlywood", weight=3]; 6003[label="gcd2 (primEqInt (primMinusNat Zero vuz366) (fromInt (Pos Zero))) (primMinusNat Zero vuz366) (Pos vuz144)",fontsize=16,color="burlywood",shape="box"];6550[label="vuz366/Succ vuz3660",fontsize=10,color="white",style="solid",shape="box"];6003 -> 6550[label="",style="solid", color="burlywood", weight=9]; 6550 -> 6026[label="",style="solid", color="burlywood", weight=3]; 6551[label="vuz366/Zero",fontsize=10,color="white",style="solid",shape="box"];6003 -> 6551[label="",style="solid", color="burlywood", weight=9]; 6551 -> 6027[label="",style="solid", color="burlywood", weight=3]; 6004 -> 1352[label="",style="dashed", color="red", weight=0]; 6004[label="primPlusNat vuz352 vuz368",fontsize=16,color="magenta"];6004 -> 6028[label="",style="dashed", color="magenta", weight=3]; 6004 -> 6029[label="",style="dashed", color="magenta", weight=3]; 4165[label="gcd2 (primEqInt (Neg vuz283) (fromInt (Pos Zero))) (Neg vuz283) (Neg vuz68)",fontsize=16,color="burlywood",shape="triangle"];6552[label="vuz283/Succ vuz2830",fontsize=10,color="white",style="solid",shape="box"];4165 -> 6552[label="",style="solid", color="burlywood", weight=9]; 6552 -> 4185[label="",style="solid", color="burlywood", weight=3]; 6553[label="vuz283/Zero",fontsize=10,color="white",style="solid",shape="box"];4165 -> 6553[label="",style="solid", color="burlywood", weight=9]; 6553 -> 4186[label="",style="solid", color="burlywood", weight=3]; 4408 -> 1352[label="",style="dashed", color="red", weight=0]; 4408[label="primPlusNat vuz285 vuz301",fontsize=16,color="magenta"];4408 -> 4423[label="",style="dashed", color="magenta", weight=3]; 4408 -> 4424[label="",style="dashed", color="magenta", weight=3]; 4409[label="gcd2 (primEqInt (primMinusNat (Succ vuz2870) vuz303) (fromInt (Pos Zero))) (primMinusNat (Succ vuz2870) vuz303) (Neg vuz68)",fontsize=16,color="burlywood",shape="box"];6554[label="vuz303/Succ vuz3030",fontsize=10,color="white",style="solid",shape="box"];4409 -> 6554[label="",style="solid", color="burlywood", weight=9]; 6554 -> 4425[label="",style="solid", color="burlywood", weight=3]; 6555[label="vuz303/Zero",fontsize=10,color="white",style="solid",shape="box"];4409 -> 6555[label="",style="solid", color="burlywood", weight=9]; 6555 -> 4426[label="",style="solid", color="burlywood", weight=3]; 4410[label="gcd2 (primEqInt (primMinusNat Zero vuz303) (fromInt (Pos Zero))) (primMinusNat Zero vuz303) (Neg vuz68)",fontsize=16,color="burlywood",shape="box"];6556[label="vuz303/Succ vuz3030",fontsize=10,color="white",style="solid",shape="box"];4410 -> 6556[label="",style="solid", color="burlywood", weight=9]; 6556 -> 4427[label="",style="solid", color="burlywood", weight=3]; 6557[label="vuz303/Zero",fontsize=10,color="white",style="solid",shape="box"];4410 -> 6557[label="",style="solid", color="burlywood", weight=9]; 6557 -> 4428[label="",style="solid", color="burlywood", weight=3]; 5011[label="vuz3410",fontsize=16,color="green",shape="box"];5012[label="vuz3400",fontsize=16,color="green",shape="box"];5013[label="Succ (primDivNatS (primMinusNatS (Succ vuz338) (Succ vuz339)) (Succ (Succ vuz339)))",fontsize=16,color="green",shape="box"];5013 -> 5037[label="",style="dashed", color="green", weight=3]; 5014[label="Zero",fontsize=16,color="green",shape="box"];5771 -> 4417[label="",style="dashed", color="red", weight=0]; 5771[label="gcd2 (primEqInt (Pos vuz347) (fromInt (Pos Zero))) (Pos vuz347) (Neg vuz71)",fontsize=16,color="magenta"];5771 -> 5790[label="",style="dashed", color="magenta", weight=3]; 5771 -> 5791[label="",style="dashed", color="magenta", weight=3]; 4418 -> 1352[label="",style="dashed", color="red", weight=0]; 4418[label="primPlusNat vuz289 vuz305",fontsize=16,color="magenta"];4418 -> 4437[label="",style="dashed", color="magenta", weight=3]; 4418 -> 4438[label="",style="dashed", color="magenta", weight=3]; 4419 -> 1352[label="",style="dashed", color="red", weight=0]; 4419[label="primPlusNat vuz289 vuz305",fontsize=16,color="magenta"];4419 -> 4439[label="",style="dashed", color="magenta", weight=3]; 4419 -> 4440[label="",style="dashed", color="magenta", weight=3]; 4417[label="gcd2 (primEqInt (Pos vuz309) (fromInt (Pos Zero))) (Pos vuz308) (Neg vuz71)",fontsize=16,color="burlywood",shape="triangle"];6558[label="vuz309/Succ vuz3090",fontsize=10,color="white",style="solid",shape="box"];4417 -> 6558[label="",style="solid", color="burlywood", weight=9]; 6558 -> 4441[label="",style="solid", color="burlywood", weight=3]; 6559[label="vuz309/Zero",fontsize=10,color="white",style="solid",shape="box"];4417 -> 6559[label="",style="solid", color="burlywood", weight=9]; 6559 -> 4442[label="",style="solid", color="burlywood", weight=3]; 4420[label="vuz291",fontsize=16,color="green",shape="box"];4421[label="vuz307",fontsize=16,color="green",shape="box"];4422[label="vuz71",fontsize=16,color="green",shape="box"];5772[label="gcd2 (primEqInt (Pos vuz348) (fromInt (Pos Zero))) (Pos vuz348) (Pos vuz74)",fontsize=16,color="burlywood",shape="triangle"];6560[label="vuz348/Succ vuz3480",fontsize=10,color="white",style="solid",shape="box"];5772 -> 6560[label="",style="solid", color="burlywood", weight=9]; 6560 -> 5792[label="",style="solid", color="burlywood", weight=3]; 6561[label="vuz348/Zero",fontsize=10,color="white",style="solid",shape="box"];5772 -> 6561[label="",style="solid", color="burlywood", weight=9]; 6561 -> 5793[label="",style="solid", color="burlywood", weight=3]; 6005[label="vuz354",fontsize=16,color="green",shape="box"];6006[label="vuz74",fontsize=16,color="green",shape="box"];6007[label="vuz370",fontsize=16,color="green",shape="box"];6008 -> 1352[label="",style="dashed", color="red", weight=0]; 6008[label="primPlusNat vuz356 vuz372",fontsize=16,color="magenta"];6008 -> 6030[label="",style="dashed", color="magenta", weight=3]; 6008 -> 6031[label="",style="dashed", color="magenta", weight=3]; 4183[label="gcd2 (primEqInt (Neg (Succ vuz2820)) (fromInt (Pos Zero))) (Neg (Succ vuz2820)) (Pos vuz144)",fontsize=16,color="black",shape="box"];4183 -> 4204[label="",style="solid", color="black", weight=3]; 4184[label="gcd2 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];4184 -> 4205[label="",style="solid", color="black", weight=3]; 6024[label="gcd2 (primEqInt (primMinusNat (Succ vuz3500) (Succ vuz3660)) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3500) (Succ vuz3660)) (Pos vuz144)",fontsize=16,color="black",shape="box"];6024 -> 6047[label="",style="solid", color="black", weight=3]; 6025[label="gcd2 (primEqInt (primMinusNat (Succ vuz3500) Zero) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3500) Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];6025 -> 6048[label="",style="solid", color="black", weight=3]; 6026[label="gcd2 (primEqInt (primMinusNat Zero (Succ vuz3660)) (fromInt (Pos Zero))) (primMinusNat Zero (Succ vuz3660)) (Pos vuz144)",fontsize=16,color="black",shape="box"];6026 -> 6049[label="",style="solid", color="black", weight=3]; 6027[label="gcd2 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (primMinusNat Zero Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];6027 -> 6050[label="",style="solid", color="black", weight=3]; 6028[label="vuz368",fontsize=16,color="green",shape="box"];6029[label="vuz352",fontsize=16,color="green",shape="box"];4185[label="gcd2 (primEqInt (Neg (Succ vuz2830)) (fromInt (Pos Zero))) (Neg (Succ vuz2830)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4185 -> 4206[label="",style="solid", color="black", weight=3]; 4186[label="gcd2 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4186 -> 4207[label="",style="solid", color="black", weight=3]; 4423[label="vuz301",fontsize=16,color="green",shape="box"];4424[label="vuz285",fontsize=16,color="green",shape="box"];4425[label="gcd2 (primEqInt (primMinusNat (Succ vuz2870) (Succ vuz3030)) (fromInt (Pos Zero))) (primMinusNat (Succ vuz2870) (Succ vuz3030)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4425 -> 4453[label="",style="solid", color="black", weight=3]; 4426[label="gcd2 (primEqInt (primMinusNat (Succ vuz2870) Zero) (fromInt (Pos Zero))) (primMinusNat (Succ vuz2870) Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4426 -> 4454[label="",style="solid", color="black", weight=3]; 4427[label="gcd2 (primEqInt (primMinusNat Zero (Succ vuz3030)) (fromInt (Pos Zero))) (primMinusNat Zero (Succ vuz3030)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4427 -> 4455[label="",style="solid", color="black", weight=3]; 4428[label="gcd2 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (primMinusNat Zero Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4428 -> 4456[label="",style="solid", color="black", weight=3]; 5037 -> 4127[label="",style="dashed", color="red", weight=0]; 5037[label="primDivNatS (primMinusNatS (Succ vuz338) (Succ vuz339)) (Succ (Succ vuz339))",fontsize=16,color="magenta"];5037 -> 5725[label="",style="dashed", color="magenta", weight=3]; 5037 -> 5726[label="",style="dashed", color="magenta", weight=3]; 5790[label="vuz347",fontsize=16,color="green",shape="box"];5791[label="vuz347",fontsize=16,color="green",shape="box"];4437[label="vuz305",fontsize=16,color="green",shape="box"];4438[label="vuz289",fontsize=16,color="green",shape="box"];4439[label="vuz305",fontsize=16,color="green",shape="box"];4440[label="vuz289",fontsize=16,color="green",shape="box"];4441[label="gcd2 (primEqInt (Pos (Succ vuz3090)) (fromInt (Pos Zero))) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4441 -> 4464[label="",style="solid", color="black", weight=3]; 4442[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4442 -> 4465[label="",style="solid", color="black", weight=3]; 5792[label="gcd2 (primEqInt (Pos (Succ vuz3480)) (fromInt (Pos Zero))) (Pos (Succ vuz3480)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5792 -> 5812[label="",style="solid", color="black", weight=3]; 5793[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz74)",fontsize=16,color="black",shape="box"];5793 -> 5813[label="",style="solid", color="black", weight=3]; 6030[label="vuz372",fontsize=16,color="green",shape="box"];6031[label="vuz356",fontsize=16,color="green",shape="box"];4204[label="gcd2 (primEqInt (Neg (Succ vuz2820)) (Pos Zero)) (Neg (Succ vuz2820)) (Pos vuz144)",fontsize=16,color="black",shape="box"];4204 -> 4287[label="",style="solid", color="black", weight=3]; 4205[label="gcd2 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];4205 -> 4288[label="",style="solid", color="black", weight=3]; 6047 -> 5954[label="",style="dashed", color="red", weight=0]; 6047[label="gcd2 (primEqInt (primMinusNat vuz3500 vuz3660) (fromInt (Pos Zero))) (primMinusNat vuz3500 vuz3660) (Pos vuz144)",fontsize=16,color="magenta"];6047 -> 6057[label="",style="dashed", color="magenta", weight=3]; 6047 -> 6058[label="",style="dashed", color="magenta", weight=3]; 6048 -> 5772[label="",style="dashed", color="red", weight=0]; 6048[label="gcd2 (primEqInt (Pos (Succ vuz3500)) (fromInt (Pos Zero))) (Pos (Succ vuz3500)) (Pos vuz144)",fontsize=16,color="magenta"];6048 -> 6059[label="",style="dashed", color="magenta", weight=3]; 6048 -> 6060[label="",style="dashed", color="magenta", weight=3]; 6049 -> 4164[label="",style="dashed", color="red", weight=0]; 6049[label="gcd2 (primEqInt (Neg (Succ vuz3660)) (fromInt (Pos Zero))) (Neg (Succ vuz3660)) (Pos vuz144)",fontsize=16,color="magenta"];6049 -> 6061[label="",style="dashed", color="magenta", weight=3]; 6050 -> 5772[label="",style="dashed", color="red", weight=0]; 6050[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz144)",fontsize=16,color="magenta"];6050 -> 6062[label="",style="dashed", color="magenta", weight=3]; 6050 -> 6063[label="",style="dashed", color="magenta", weight=3]; 4206[label="gcd2 (primEqInt (Neg (Succ vuz2830)) (Pos Zero)) (Neg (Succ vuz2830)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4206 -> 4289[label="",style="solid", color="black", weight=3]; 4207[label="gcd2 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4207 -> 4290[label="",style="solid", color="black", weight=3]; 4453 -> 4366[label="",style="dashed", color="red", weight=0]; 4453[label="gcd2 (primEqInt (primMinusNat vuz2870 vuz3030) (fromInt (Pos Zero))) (primMinusNat vuz2870 vuz3030) (Neg vuz68)",fontsize=16,color="magenta"];4453 -> 4476[label="",style="dashed", color="magenta", weight=3]; 4453 -> 4477[label="",style="dashed", color="magenta", weight=3]; 4454 -> 4417[label="",style="dashed", color="red", weight=0]; 4454[label="gcd2 (primEqInt (Pos (Succ vuz2870)) (fromInt (Pos Zero))) (Pos (Succ vuz2870)) (Neg vuz68)",fontsize=16,color="magenta"];4454 -> 4478[label="",style="dashed", color="magenta", weight=3]; 4454 -> 4479[label="",style="dashed", color="magenta", weight=3]; 4454 -> 4480[label="",style="dashed", color="magenta", weight=3]; 4455 -> 4165[label="",style="dashed", color="red", weight=0]; 4455[label="gcd2 (primEqInt (Neg (Succ vuz3030)) (fromInt (Pos Zero))) (Neg (Succ vuz3030)) (Neg vuz68)",fontsize=16,color="magenta"];4455 -> 4481[label="",style="dashed", color="magenta", weight=3]; 4456 -> 4417[label="",style="dashed", color="red", weight=0]; 4456[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Neg vuz68)",fontsize=16,color="magenta"];4456 -> 4482[label="",style="dashed", color="magenta", weight=3]; 4456 -> 4483[label="",style="dashed", color="magenta", weight=3]; 4456 -> 4484[label="",style="dashed", color="magenta", weight=3]; 5725[label="Succ vuz339",fontsize=16,color="green",shape="box"];5726[label="primMinusNatS (Succ vuz338) (Succ vuz339)",fontsize=16,color="black",shape="box"];5726 -> 5741[label="",style="solid", color="black", weight=3]; 4464[label="gcd2 (primEqInt (Pos (Succ vuz3090)) (Pos Zero)) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4464 -> 4492[label="",style="solid", color="black", weight=3]; 4465[label="gcd2 (primEqInt (Pos Zero) (Pos Zero)) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4465 -> 4493[label="",style="solid", color="black", weight=3]; 5812[label="gcd2 (primEqInt (Pos (Succ vuz3480)) (Pos Zero)) (Pos (Succ vuz3480)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5812 -> 5888[label="",style="solid", color="black", weight=3]; 5813[label="gcd2 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (Pos vuz74)",fontsize=16,color="black",shape="box"];5813 -> 5889[label="",style="solid", color="black", weight=3]; 4287[label="gcd2 False (Neg (Succ vuz2820)) (Pos vuz144)",fontsize=16,color="black",shape="box"];4287 -> 4309[label="",style="solid", color="black", weight=3]; 4288[label="gcd2 True (Neg Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];4288 -> 4310[label="",style="solid", color="black", weight=3]; 6057[label="vuz3660",fontsize=16,color="green",shape="box"];6058[label="vuz3500",fontsize=16,color="green",shape="box"];6059[label="vuz144",fontsize=16,color="green",shape="box"];6060[label="Succ vuz3500",fontsize=16,color="green",shape="box"];6061[label="Succ vuz3660",fontsize=16,color="green",shape="box"];6062[label="vuz144",fontsize=16,color="green",shape="box"];6063[label="Zero",fontsize=16,color="green",shape="box"];4289[label="gcd2 False (Neg (Succ vuz2830)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4289 -> 4311[label="",style="solid", color="black", weight=3]; 4290[label="gcd2 True (Neg Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4290 -> 4312[label="",style="solid", color="black", weight=3]; 4476[label="vuz3030",fontsize=16,color="green",shape="box"];4477[label="vuz2870",fontsize=16,color="green",shape="box"];4478[label="Succ vuz2870",fontsize=16,color="green",shape="box"];4479[label="Succ vuz2870",fontsize=16,color="green",shape="box"];4480[label="vuz68",fontsize=16,color="green",shape="box"];4481[label="Succ vuz3030",fontsize=16,color="green",shape="box"];4482[label="Zero",fontsize=16,color="green",shape="box"];4483[label="Zero",fontsize=16,color="green",shape="box"];4484[label="vuz68",fontsize=16,color="green",shape="box"];5741[label="primMinusNatS vuz338 vuz339",fontsize=16,color="burlywood",shape="triangle"];6562[label="vuz338/Succ vuz3380",fontsize=10,color="white",style="solid",shape="box"];5741 -> 6562[label="",style="solid", color="burlywood", weight=9]; 6562 -> 5758[label="",style="solid", color="burlywood", weight=3]; 6563[label="vuz338/Zero",fontsize=10,color="white",style="solid",shape="box"];5741 -> 6563[label="",style="solid", color="burlywood", weight=9]; 6563 -> 5759[label="",style="solid", color="burlywood", weight=3]; 4492[label="gcd2 False (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4492 -> 4515[label="",style="solid", color="black", weight=3]; 4493[label="gcd2 True (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4493 -> 4516[label="",style="solid", color="black", weight=3]; 5888[label="gcd2 False (Pos (Succ vuz3480)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5888 -> 5906[label="",style="solid", color="black", weight=3]; 5889[label="gcd2 True (Pos Zero) (Pos vuz74)",fontsize=16,color="black",shape="box"];5889 -> 5907[label="",style="solid", color="black", weight=3]; 4309[label="gcd0 (Neg (Succ vuz2820)) (Pos vuz144)",fontsize=16,color="black",shape="box"];4309 -> 4400[label="",style="solid", color="black", weight=3]; 4310[label="gcd1 (Pos vuz144 == fromInt (Pos Zero)) (Neg Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];4310 -> 4401[label="",style="solid", color="black", weight=3]; 4311[label="gcd0 (Neg (Succ vuz2830)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4311 -> 4402[label="",style="solid", color="black", weight=3]; 4312[label="gcd1 (Neg vuz68 == fromInt (Pos Zero)) (Neg Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4312 -> 4403[label="",style="solid", color="black", weight=3]; 5758[label="primMinusNatS (Succ vuz3380) vuz339",fontsize=16,color="burlywood",shape="box"];6564[label="vuz339/Succ vuz3390",fontsize=10,color="white",style="solid",shape="box"];5758 -> 6564[label="",style="solid", color="burlywood", weight=9]; 6564 -> 5773[label="",style="solid", color="burlywood", weight=3]; 6565[label="vuz339/Zero",fontsize=10,color="white",style="solid",shape="box"];5758 -> 6565[label="",style="solid", color="burlywood", weight=9]; 6565 -> 5774[label="",style="solid", color="burlywood", weight=3]; 5759[label="primMinusNatS Zero vuz339",fontsize=16,color="burlywood",shape="box"];6566[label="vuz339/Succ vuz3390",fontsize=10,color="white",style="solid",shape="box"];5759 -> 6566[label="",style="solid", color="burlywood", weight=9]; 6566 -> 5775[label="",style="solid", color="burlywood", weight=3]; 6567[label="vuz339/Zero",fontsize=10,color="white",style="solid",shape="box"];5759 -> 6567[label="",style="solid", color="burlywood", weight=9]; 6567 -> 5776[label="",style="solid", color="burlywood", weight=3]; 4515[label="gcd0 (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4515 -> 4537[label="",style="solid", color="black", weight=3]; 4516[label="gcd1 (Neg vuz71 == fromInt (Pos Zero)) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4516 -> 4538[label="",style="solid", color="black", weight=3]; 5906[label="gcd0 (Pos (Succ vuz3480)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5906 -> 5986[label="",style="solid", color="black", weight=3]; 5907[label="gcd1 (Pos vuz74 == fromInt (Pos Zero)) (Pos Zero) (Pos vuz74)",fontsize=16,color="black",shape="box"];5907 -> 5987[label="",style="solid", color="black", weight=3]; 4400 -> 6009[label="",style="dashed", color="red", weight=0]; 4400[label="gcd0Gcd' (abs (Neg (Succ vuz2820))) (abs (Pos vuz144))",fontsize=16,color="magenta"];4400 -> 6010[label="",style="dashed", color="magenta", weight=3]; 4400 -> 6011[label="",style="dashed", color="magenta", weight=3]; 4401[label="gcd1 (primEqInt (Pos vuz144) (fromInt (Pos Zero))) (Neg Zero) (Pos vuz144)",fontsize=16,color="burlywood",shape="box"];6568[label="vuz144/Succ vuz1440",fontsize=10,color="white",style="solid",shape="box"];4401 -> 6568[label="",style="solid", color="burlywood", weight=9]; 6568 -> 4444[label="",style="solid", color="burlywood", weight=3]; 6569[label="vuz144/Zero",fontsize=10,color="white",style="solid",shape="box"];4401 -> 6569[label="",style="solid", color="burlywood", weight=9]; 6569 -> 4445[label="",style="solid", color="burlywood", weight=3]; 4402 -> 6009[label="",style="dashed", color="red", weight=0]; 4402[label="gcd0Gcd' (abs (Neg (Succ vuz2830))) (abs (Neg vuz68))",fontsize=16,color="magenta"];4402 -> 6012[label="",style="dashed", color="magenta", weight=3]; 4402 -> 6013[label="",style="dashed", color="magenta", weight=3]; 4403[label="gcd1 (primEqInt (Neg vuz68) (fromInt (Pos Zero))) (Neg Zero) (Neg vuz68)",fontsize=16,color="burlywood",shape="box"];6570[label="vuz68/Succ vuz680",fontsize=10,color="white",style="solid",shape="box"];4403 -> 6570[label="",style="solid", color="burlywood", weight=9]; 6570 -> 4447[label="",style="solid", color="burlywood", weight=3]; 6571[label="vuz68/Zero",fontsize=10,color="white",style="solid",shape="box"];4403 -> 6571[label="",style="solid", color="burlywood", weight=9]; 6571 -> 4448[label="",style="solid", color="burlywood", weight=3]; 5773[label="primMinusNatS (Succ vuz3380) (Succ vuz3390)",fontsize=16,color="black",shape="box"];5773 -> 5794[label="",style="solid", color="black", weight=3]; 5774[label="primMinusNatS (Succ vuz3380) Zero",fontsize=16,color="black",shape="box"];5774 -> 5795[label="",style="solid", color="black", weight=3]; 5775[label="primMinusNatS Zero (Succ vuz3390)",fontsize=16,color="black",shape="box"];5775 -> 5796[label="",style="solid", color="black", weight=3]; 5776[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="box"];5776 -> 5797[label="",style="solid", color="black", weight=3]; 4537 -> 6009[label="",style="dashed", color="red", weight=0]; 4537[label="gcd0Gcd' (abs (Pos vuz308)) (abs (Neg vuz71))",fontsize=16,color="magenta"];4537 -> 6014[label="",style="dashed", color="magenta", weight=3]; 4537 -> 6015[label="",style="dashed", color="magenta", weight=3]; 4538[label="gcd1 (primEqInt (Neg vuz71) (fromInt (Pos Zero))) (Pos vuz308) (Neg vuz71)",fontsize=16,color="burlywood",shape="box"];6572[label="vuz71/Succ vuz710",fontsize=10,color="white",style="solid",shape="box"];4538 -> 6572[label="",style="solid", color="burlywood", weight=9]; 6572 -> 4557[label="",style="solid", color="burlywood", weight=3]; 6573[label="vuz71/Zero",fontsize=10,color="white",style="solid",shape="box"];4538 -> 6573[label="",style="solid", color="burlywood", weight=9]; 6573 -> 4558[label="",style="solid", color="burlywood", weight=3]; 5986 -> 6009[label="",style="dashed", color="red", weight=0]; 5986[label="gcd0Gcd' (abs (Pos (Succ vuz3480))) (abs (Pos vuz74))",fontsize=16,color="magenta"];5986 -> 6016[label="",style="dashed", color="magenta", weight=3]; 5986 -> 6017[label="",style="dashed", color="magenta", weight=3]; 5987[label="gcd1 (primEqInt (Pos vuz74) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz74)",fontsize=16,color="burlywood",shape="box"];6574[label="vuz74/Succ 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4467[label="",style="solid", color="black", weight=3]; 4445[label="gcd1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];4445 -> 4468[label="",style="solid", color="black", weight=3]; 6012 -> 6010[label="",style="dashed", color="red", weight=0]; 6012[label="abs (Neg (Succ vuz2830))",fontsize=16,color="magenta"];6012 -> 6037[label="",style="dashed", color="magenta", weight=3]; 6013[label="abs (Neg vuz68)",fontsize=16,color="black",shape="triangle"];6013 -> 6038[label="",style="solid", color="black", weight=3]; 4447[label="gcd1 (primEqInt (Neg (Succ vuz680)) (fromInt (Pos Zero))) (Neg Zero) (Neg (Succ vuz680))",fontsize=16,color="black",shape="box"];4447 -> 4470[label="",style="solid", color="black", weight=3]; 4448[label="gcd1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];4448 -> 4471[label="",style="solid", color="black", weight=3]; 5794 -> 5741[label="",style="dashed", color="red", weight=0]; 5794[label="primMinusNatS vuz3380 vuz3390",fontsize=16,color="magenta"];5794 -> 5814[label="",style="dashed", color="magenta", weight=3]; 5794 -> 5815[label="",style="dashed", color="magenta", weight=3]; 5795[label="Succ vuz3380",fontsize=16,color="green",shape="box"];5796[label="Zero",fontsize=16,color="green",shape="box"];5797[label="Zero",fontsize=16,color="green",shape="box"];6014 -> 6011[label="",style="dashed", color="red", weight=0]; 6014[label="abs (Pos vuz308)",fontsize=16,color="magenta"];6014 -> 6039[label="",style="dashed", color="magenta", weight=3]; 6015 -> 6013[label="",style="dashed", color="red", weight=0]; 6015[label="abs (Neg vuz71)",fontsize=16,color="magenta"];6015 -> 6040[label="",style="dashed", color="magenta", weight=3]; 4557[label="gcd1 (primEqInt (Neg (Succ vuz710)) (fromInt (Pos Zero))) (Pos vuz308) (Neg (Succ vuz710))",fontsize=16,color="black",shape="box"];4557 -> 4577[label="",style="solid", color="black", weight=3]; 4558[label="gcd1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Pos vuz308) (Neg Zero)",fontsize=16,color="black",shape="box"];4558 -> 4578[label="",style="solid", color="black", weight=3]; 6016 -> 6011[label="",style="dashed", color="red", weight=0]; 6016[label="abs (Pos (Succ vuz3480))",fontsize=16,color="magenta"];6016 -> 6041[label="",style="dashed", color="magenta", weight=3]; 6017 -> 6011[label="",style="dashed", color="red", weight=0]; 6017[label="abs (Pos vuz74)",fontsize=16,color="magenta"];6017 -> 6042[label="",style="dashed", color="magenta", weight=3]; 6032[label="gcd1 (primEqInt (Pos (Succ vuz740)) (fromInt (Pos Zero))) (Pos Zero) (Pos (Succ vuz740))",fontsize=16,color="black",shape="box"];6032 -> 6051[label="",style="solid", color="black", weight=3]; 6033[label="gcd1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];6033 -> 6052[label="",style="solid", color="black", weight=3]; 6034[label="absReal (Neg (Succ vuz2820))",fontsize=16,color="black",shape="box"];6034 -> 6053[label="",style="solid", color="black", weight=3]; 6035[label="absReal (Pos vuz144)",fontsize=16,color="black",shape="box"];6035 -> 6054[label="",style="solid", color="black", weight=3]; 6036[label="gcd0Gcd'2 vuz374 vuz373",fontsize=16,color="black",shape="box"];6036 -> 6055[label="",style="solid", color="black", weight=3]; 4467[label="gcd1 (primEqInt (Pos (Succ vuz1440)) (Pos Zero)) (Neg Zero) (Pos (Succ vuz1440))",fontsize=16,color="black",shape="box"];4467 -> 4495[label="",style="solid", color="black", weight=3]; 4468[label="gcd1 (primEqInt (Pos Zero) (Pos Zero)) (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];4468 -> 4496[label="",style="solid", color="black", weight=3]; 6037[label="vuz2830",fontsize=16,color="green",shape="box"];6038[label="absReal (Neg vuz68)",fontsize=16,color="black",shape="box"];6038 -> 6056[label="",style="solid", color="black", weight=3]; 4470[label="gcd1 (primEqInt (Neg (Succ vuz680)) (Pos Zero)) (Neg Zero) (Neg (Succ vuz680))",fontsize=16,color="black",shape="box"];4470 -> 4498[label="",style="solid", color="black", weight=3]; 4471[label="gcd1 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];4471 -> 4499[label="",style="solid", color="black", weight=3]; 5814[label="vuz3380",fontsize=16,color="green",shape="box"];5815[label="vuz3390",fontsize=16,color="green",shape="box"];6039[label="vuz308",fontsize=16,color="green",shape="box"];6040[label="vuz71",fontsize=16,color="green",shape="box"];4577[label="gcd1 (primEqInt (Neg (Succ vuz710)) (Pos Zero)) (Pos vuz308) (Neg (Succ vuz710))",fontsize=16,color="black",shape="box"];4577 -> 4600[label="",style="solid", color="black", weight=3]; 4578[label="gcd1 (primEqInt (Neg Zero) (Pos Zero)) (Pos vuz308) (Neg Zero)",fontsize=16,color="black",shape="box"];4578 -> 4601[label="",style="solid", color="black", weight=3]; 6041[label="Succ vuz3480",fontsize=16,color="green",shape="box"];6042[label="vuz74",fontsize=16,color="green",shape="box"];6051[label="gcd1 (primEqInt (Pos (Succ vuz740)) (Pos Zero)) (Pos Zero) (Pos (Succ vuz740))",fontsize=16,color="black",shape="box"];6051 -> 6064[label="",style="solid", color="black", weight=3]; 6052[label="gcd1 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];6052 -> 6065[label="",style="solid", color="black", weight=3]; 6053[label="absReal2 (Neg (Succ vuz2820))",fontsize=16,color="black",shape="box"];6053 -> 6066[label="",style="solid", color="black", weight=3]; 6054[label="absReal2 (Pos vuz144)",fontsize=16,color="black",shape="box"];6054 -> 6067[label="",style="solid", color="black", weight=3]; 6055[label="gcd0Gcd'1 (vuz373 == fromInt (Pos Zero)) vuz374 vuz373",fontsize=16,color="black",shape="box"];6055 -> 6068[label="",style="solid", color="black", weight=3]; 4495[label="gcd1 False (Neg Zero) (Pos (Succ vuz1440))",fontsize=16,color="black",shape="box"];4495 -> 4518[label="",style="solid", color="black", weight=3]; 4496[label="gcd1 True (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];4496 -> 4519[label="",style="solid", color="black", weight=3]; 6056[label="absReal2 (Neg vuz68)",fontsize=16,color="black",shape="box"];6056 -> 6069[label="",style="solid", color="black", weight=3]; 4498[label="gcd1 False (Neg Zero) (Neg (Succ vuz680))",fontsize=16,color="black",shape="box"];4498 -> 4521[label="",style="solid", color="black", weight=3]; 4499[label="gcd1 True (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];4499 -> 4522[label="",style="solid", color="black", weight=3]; 4600[label="gcd1 False (Pos vuz308) (Neg (Succ vuz710))",fontsize=16,color="black",shape="box"];4600 -> 4623[label="",style="solid", color="black", weight=3]; 4601[label="gcd1 True (Pos vuz308) (Neg Zero)",fontsize=16,color="black",shape="box"];4601 -> 4624[label="",style="solid", color="black", weight=3]; 6064[label="gcd1 False (Pos Zero) (Pos (Succ vuz740))",fontsize=16,color="black",shape="box"];6064 -> 6070[label="",style="solid", color="black", weight=3]; 6065[label="gcd1 True (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];6065 -> 6071[label="",style="solid", color="black", weight=3]; 6066[label="absReal1 (Neg (Succ vuz2820)) (Neg (Succ vuz2820) >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6066 -> 6072[label="",style="solid", color="black", weight=3]; 6067[label="absReal1 (Pos vuz144) (Pos vuz144 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6067 -> 6073[label="",style="solid", color="black", weight=3]; 6068[label="gcd0Gcd'1 (primEqInt vuz373 (fromInt (Pos Zero))) vuz374 vuz373",fontsize=16,color="burlywood",shape="box"];6576[label="vuz373/Pos vuz3730",fontsize=10,color="white",style="solid",shape="box"];6068 -> 6576[label="",style="solid", color="burlywood", weight=9]; 6576 -> 6074[label="",style="solid", color="burlywood", weight=3]; 6577[label="vuz373/Neg vuz3730",fontsize=10,color="white",style="solid",shape="box"];6068 -> 6577[label="",style="solid", color="burlywood", weight=9]; 6577 -> 6075[label="",style="solid", color="burlywood", weight=3]; 4518[label="gcd0 (Neg Zero) (Pos (Succ vuz1440))",fontsize=16,color="black",shape="box"];4518 -> 4540[label="",style="solid", color="black", weight=3]; 4519 -> 4106[label="",style="dashed", color="red", weight=0]; 4519[label="error []",fontsize=16,color="magenta"];6069[label="absReal1 (Neg vuz68) (Neg vuz68 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6069 -> 6076[label="",style="solid", color="black", weight=3]; 4521[label="gcd0 (Neg Zero) (Neg (Succ vuz680))",fontsize=16,color="black",shape="box"];4521 -> 4542[label="",style="solid", color="black", weight=3]; 4522 -> 4106[label="",style="dashed", color="red", weight=0]; 4522[label="error []",fontsize=16,color="magenta"];4623 -> 4515[label="",style="dashed", color="red", weight=0]; 4623[label="gcd0 (Pos vuz308) (Neg (Succ vuz710))",fontsize=16,color="magenta"];4623 -> 4646[label="",style="dashed", color="magenta", weight=3]; 4624 -> 4106[label="",style="dashed", color="red", weight=0]; 4624[label="error []",fontsize=16,color="magenta"];6070[label="gcd0 (Pos Zero) (Pos (Succ vuz740))",fontsize=16,color="black",shape="box"];6070 -> 6077[label="",style="solid", color="black", weight=3]; 6071 -> 4106[label="",style="dashed", color="red", weight=0]; 6071[label="error []",fontsize=16,color="magenta"];6072[label="absReal1 (Neg (Succ vuz2820)) (compare (Neg (Succ vuz2820)) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];6072 -> 6078[label="",style="solid", color="black", weight=3]; 6073[label="absReal1 (Pos vuz144) (compare (Pos vuz144) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];6073 -> 6079[label="",style="solid", color="black", weight=3]; 6074[label="gcd0Gcd'1 (primEqInt (Pos vuz3730) (fromInt (Pos Zero))) vuz374 (Pos vuz3730)",fontsize=16,color="burlywood",shape="box"];6578[label="vuz3730/Succ vuz37300",fontsize=10,color="white",style="solid",shape="box"];6074 -> 6578[label="",style="solid", color="burlywood", weight=9]; 6578 -> 6080[label="",style="solid", color="burlywood", weight=3]; 6579[label="vuz3730/Zero",fontsize=10,color="white",style="solid",shape="box"];6074 -> 6579[label="",style="solid", color="burlywood", weight=9]; 6579 -> 6081[label="",style="solid", color="burlywood", weight=3]; 6075[label="gcd0Gcd'1 (primEqInt (Neg vuz3730) (fromInt (Pos Zero))) vuz374 (Neg vuz3730)",fontsize=16,color="burlywood",shape="box"];6580[label="vuz3730/Succ vuz37300",fontsize=10,color="white",style="solid",shape="box"];6075 -> 6580[label="",style="solid", color="burlywood", weight=9]; 6580 -> 6082[label="",style="solid", color="burlywood", weight=3]; 6581[label="vuz3730/Zero",fontsize=10,color="white",style="solid",shape="box"];6075 -> 6581[label="",style="solid", color="burlywood", weight=9]; 6581 -> 6083[label="",style="solid", color="burlywood", weight=3]; 4540 -> 6009[label="",style="dashed", color="red", weight=0]; 4540[label="gcd0Gcd' (abs (Neg Zero)) (abs (Pos (Succ vuz1440)))",fontsize=16,color="magenta"];4540 -> 6018[label="",style="dashed", color="magenta", weight=3]; 4540 -> 6019[label="",style="dashed", color="magenta", weight=3]; 6076[label="absReal1 (Neg vuz68) (compare (Neg vuz68) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];6076 -> 6084[label="",style="solid", color="black", weight=3]; 4542 -> 6009[label="",style="dashed", color="red", weight=0]; 4542[label="gcd0Gcd' (abs (Neg Zero)) (abs (Neg (Succ vuz680)))",fontsize=16,color="magenta"];4542 -> 6020[label="",style="dashed", color="magenta", weight=3]; 4542 -> 6021[label="",style="dashed", color="magenta", weight=3]; 4646[label="Succ vuz710",fontsize=16,color="green",shape="box"];6077 -> 6009[label="",style="dashed", color="red", weight=0]; 6077[label="gcd0Gcd' (abs (Pos Zero)) (abs (Pos (Succ vuz740)))",fontsize=16,color="magenta"];6077 -> 6085[label="",style="dashed", color="magenta", weight=3]; 6077 -> 6086[label="",style="dashed", color="magenta", weight=3]; 6078[label="absReal1 (Neg (Succ vuz2820)) (not (compare (Neg (Succ vuz2820)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6078 -> 6087[label="",style="solid", color="black", weight=3]; 6079[label="absReal1 (Pos vuz144) (not (compare (Pos vuz144) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6079 -> 6088[label="",style="solid", color="black", weight=3]; 6080[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz37300)) (fromInt (Pos Zero))) vuz374 (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6080 -> 6089[label="",style="solid", color="black", weight=3]; 6081[label="gcd0Gcd'1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz374 (Pos Zero)",fontsize=16,color="black",shape="box"];6081 -> 6090[label="",style="solid", color="black", weight=3]; 6082[label="gcd0Gcd'1 (primEqInt (Neg (Succ vuz37300)) (fromInt (Pos Zero))) vuz374 (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6082 -> 6091[label="",style="solid", color="black", weight=3]; 6083[label="gcd0Gcd'1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) vuz374 (Neg Zero)",fontsize=16,color="black",shape="box"];6083 -> 6092[label="",style="solid", color="black", weight=3]; 6018 -> 6013[label="",style="dashed", color="red", weight=0]; 6018[label="abs (Neg Zero)",fontsize=16,color="magenta"];6018 -> 6043[label="",style="dashed", color="magenta", weight=3]; 6019 -> 6011[label="",style="dashed", color="red", weight=0]; 6019[label="abs (Pos (Succ vuz1440))",fontsize=16,color="magenta"];6019 -> 6044[label="",style="dashed", color="magenta", weight=3]; 6084[label="absReal1 (Neg vuz68) (not (compare (Neg vuz68) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6084 -> 6093[label="",style="solid", color="black", weight=3]; 6020 -> 6013[label="",style="dashed", color="red", weight=0]; 6020[label="abs (Neg Zero)",fontsize=16,color="magenta"];6020 -> 6045[label="",style="dashed", color="magenta", weight=3]; 6021 -> 6013[label="",style="dashed", color="red", weight=0]; 6021[label="abs (Neg (Succ vuz680))",fontsize=16,color="magenta"];6021 -> 6046[label="",style="dashed", color="magenta", weight=3]; 6085 -> 6011[label="",style="dashed", color="red", weight=0]; 6085[label="abs (Pos Zero)",fontsize=16,color="magenta"];6085 -> 6094[label="",style="dashed", color="magenta", weight=3]; 6086 -> 6011[label="",style="dashed", color="red", weight=0]; 6086[label="abs (Pos (Succ vuz740))",fontsize=16,color="magenta"];6086 -> 6095[label="",style="dashed", color="magenta", weight=3]; 6087[label="absReal1 (Neg (Succ vuz2820)) (not (primCmpInt (Neg (Succ vuz2820)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6087 -> 6096[label="",style="solid", color="black", weight=3]; 6088[label="absReal1 (Pos vuz144) (not (primCmpInt (Pos vuz144) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];6582[label="vuz144/Succ vuz1440",fontsize=10,color="white",style="solid",shape="box"];6088 -> 6582[label="",style="solid", color="burlywood", weight=9]; 6582 -> 6097[label="",style="solid", color="burlywood", weight=3]; 6583[label="vuz144/Zero",fontsize=10,color="white",style="solid",shape="box"];6088 -> 6583[label="",style="solid", color="burlywood", weight=9]; 6583 -> 6098[label="",style="solid", color="burlywood", weight=3]; 6089[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz37300)) (Pos Zero)) vuz374 (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6089 -> 6099[label="",style="solid", color="black", weight=3]; 6090[label="gcd0Gcd'1 (primEqInt (Pos Zero) (Pos Zero)) vuz374 (Pos Zero)",fontsize=16,color="black",shape="box"];6090 -> 6100[label="",style="solid", color="black", weight=3]; 6091[label="gcd0Gcd'1 (primEqInt (Neg (Succ vuz37300)) (Pos Zero)) vuz374 (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6091 -> 6101[label="",style="solid", color="black", weight=3]; 6092[label="gcd0Gcd'1 (primEqInt (Neg Zero) (Pos Zero)) vuz374 (Neg Zero)",fontsize=16,color="black",shape="box"];6092 -> 6102[label="",style="solid", color="black", weight=3]; 6043[label="Zero",fontsize=16,color="green",shape="box"];6044[label="Succ vuz1440",fontsize=16,color="green",shape="box"];6093[label="absReal1 (Neg vuz68) (not (primCmpInt (Neg vuz68) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];6584[label="vuz68/Succ vuz680",fontsize=10,color="white",style="solid",shape="box"];6093 -> 6584[label="",style="solid", color="burlywood", weight=9]; 6584 -> 6103[label="",style="solid", color="burlywood", weight=3]; 6585[label="vuz68/Zero",fontsize=10,color="white",style="solid",shape="box"];6093 -> 6585[label="",style="solid", color="burlywood", weight=9]; 6585 -> 6104[label="",style="solid", color="burlywood", weight=3]; 6045[label="Zero",fontsize=16,color="green",shape="box"];6046[label="Succ vuz680",fontsize=16,color="green",shape="box"];6094[label="Zero",fontsize=16,color="green",shape="box"];6095[label="Succ vuz740",fontsize=16,color="green",shape="box"];6096[label="absReal1 (Neg (Succ vuz2820)) (not (primCmpInt (Neg (Succ vuz2820)) (Pos Zero) == LT))",fontsize=16,color="black",shape="triangle"];6096 -> 6105[label="",style="solid", color="black", weight=3]; 6097[label="absReal1 (Pos (Succ vuz1440)) (not (primCmpInt (Pos (Succ vuz1440)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6097 -> 6106[label="",style="solid", color="black", weight=3]; 6098[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6098 -> 6107[label="",style="solid", color="black", weight=3]; 6099[label="gcd0Gcd'1 False vuz374 (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6099 -> 6108[label="",style="solid", color="black", weight=3]; 6100[label="gcd0Gcd'1 True vuz374 (Pos Zero)",fontsize=16,color="black",shape="box"];6100 -> 6109[label="",style="solid", color="black", weight=3]; 6101[label="gcd0Gcd'1 False vuz374 (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6101 -> 6110[label="",style="solid", color="black", weight=3]; 6102[label="gcd0Gcd'1 True vuz374 (Neg Zero)",fontsize=16,color="black",shape="box"];6102 -> 6111[label="",style="solid", color="black", weight=3]; 6103[label="absReal1 (Neg (Succ vuz680)) (not (primCmpInt (Neg (Succ vuz680)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6103 -> 6112[label="",style="solid", color="black", weight=3]; 6104[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6104 -> 6113[label="",style="solid", color="black", weight=3]; 6105[label="absReal1 (Neg (Succ vuz2820)) (not (LT == LT))",fontsize=16,color="black",shape="box"];6105 -> 6114[label="",style="solid", color="black", weight=3]; 6106[label="absReal1 (Pos (Succ vuz1440)) (not (primCmpInt (Pos (Succ vuz1440)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];6106 -> 6115[label="",style="solid", color="black", weight=3]; 6107[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];6107 -> 6116[label="",style="solid", color="black", weight=3]; 6108[label="gcd0Gcd'0 vuz374 (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6108 -> 6117[label="",style="solid", color="black", weight=3]; 6109[label="vuz374",fontsize=16,color="green",shape="box"];6110[label="gcd0Gcd'0 vuz374 (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6110 -> 6118[label="",style="solid", color="black", weight=3]; 6111[label="vuz374",fontsize=16,color="green",shape="box"];6112 -> 6096[label="",style="dashed", color="red", weight=0]; 6112[label="absReal1 (Neg (Succ vuz680)) (not (primCmpInt (Neg (Succ vuz680)) (Pos Zero) == LT))",fontsize=16,color="magenta"];6112 -> 6119[label="",style="dashed", color="magenta", weight=3]; 6113[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];6113 -> 6120[label="",style="solid", color="black", weight=3]; 6114[label="absReal1 (Neg (Succ vuz2820)) (not True)",fontsize=16,color="black",shape="box"];6114 -> 6121[label="",style="solid", color="black", weight=3]; 6115[label="absReal1 (Pos (Succ vuz1440)) (not (primCmpNat (Succ vuz1440) Zero == LT))",fontsize=16,color="black",shape="box"];6115 -> 6122[label="",style="solid", color="black", weight=3]; 6116[label="absReal1 (Pos Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];6116 -> 6123[label="",style="solid", color="black", weight=3]; 6117 -> 6009[label="",style="dashed", color="red", weight=0]; 6117[label="gcd0Gcd' (Pos (Succ vuz37300)) (vuz374 `rem` Pos (Succ vuz37300))",fontsize=16,color="magenta"];6117 -> 6124[label="",style="dashed", color="magenta", weight=3]; 6117 -> 6125[label="",style="dashed", color="magenta", weight=3]; 6118 -> 6009[label="",style="dashed", color="red", weight=0]; 6118[label="gcd0Gcd' (Neg (Succ vuz37300)) (vuz374 `rem` Neg (Succ vuz37300))",fontsize=16,color="magenta"];6118 -> 6126[label="",style="dashed", color="magenta", weight=3]; 6118 -> 6127[label="",style="dashed", color="magenta", weight=3]; 6119[label="vuz680",fontsize=16,color="green",shape="box"];6120[label="absReal1 (Neg Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];6120 -> 6128[label="",style="solid", color="black", weight=3]; 6121[label="absReal1 (Neg (Succ vuz2820)) False",fontsize=16,color="black",shape="box"];6121 -> 6129[label="",style="solid", color="black", weight=3]; 6122[label="absReal1 (Pos (Succ vuz1440)) (not (GT == LT))",fontsize=16,color="black",shape="box"];6122 -> 6130[label="",style="solid", color="black", weight=3]; 6123[label="absReal1 (Pos Zero) (not False)",fontsize=16,color="black",shape="box"];6123 -> 6131[label="",style="solid", color="black", weight=3]; 6124[label="Pos (Succ vuz37300)",fontsize=16,color="green",shape="box"];6125[label="vuz374 `rem` Pos (Succ vuz37300)",fontsize=16,color="black",shape="box"];6125 -> 6132[label="",style="solid", color="black", weight=3]; 6126[label="Neg (Succ vuz37300)",fontsize=16,color="green",shape="box"];6127[label="vuz374 `rem` Neg (Succ vuz37300)",fontsize=16,color="black",shape="box"];6127 -> 6133[label="",style="solid", color="black", weight=3]; 6128[label="absReal1 (Neg Zero) (not False)",fontsize=16,color="black",shape="box"];6128 -> 6134[label="",style="solid", color="black", weight=3]; 6129[label="absReal0 (Neg (Succ vuz2820)) otherwise",fontsize=16,color="black",shape="box"];6129 -> 6135[label="",style="solid", color="black", weight=3]; 6130[label="absReal1 (Pos (Succ vuz1440)) (not False)",fontsize=16,color="black",shape="box"];6130 -> 6136[label="",style="solid", color="black", weight=3]; 6131[label="absReal1 (Pos Zero) True",fontsize=16,color="black",shape="box"];6131 -> 6137[label="",style="solid", color="black", weight=3]; 6132[label="primRemInt vuz374 (Pos (Succ vuz37300))",fontsize=16,color="burlywood",shape="box"];6586[label="vuz374/Pos vuz3740",fontsize=10,color="white",style="solid",shape="box"];6132 -> 6586[label="",style="solid", color="burlywood", weight=9]; 6586 -> 6138[label="",style="solid", color="burlywood", weight=3]; 6587[label="vuz374/Neg vuz3740",fontsize=10,color="white",style="solid",shape="box"];6132 -> 6587[label="",style="solid", color="burlywood", weight=9]; 6587 -> 6139[label="",style="solid", color="burlywood", weight=3]; 6133[label="primRemInt vuz374 (Neg (Succ vuz37300))",fontsize=16,color="burlywood",shape="box"];6588[label="vuz374/Pos vuz3740",fontsize=10,color="white",style="solid",shape="box"];6133 -> 6588[label="",style="solid", color="burlywood", weight=9]; 6588 -> 6140[label="",style="solid", color="burlywood", weight=3]; 6589[label="vuz374/Neg vuz3740",fontsize=10,color="white",style="solid",shape="box"];6133 -> 6589[label="",style="solid", color="burlywood", weight=9]; 6589 -> 6141[label="",style="solid", color="burlywood", weight=3]; 6134[label="absReal1 (Neg Zero) True",fontsize=16,color="black",shape="box"];6134 -> 6142[label="",style="solid", color="black", weight=3]; 6135[label="absReal0 (Neg (Succ vuz2820)) True",fontsize=16,color="black",shape="box"];6135 -> 6143[label="",style="solid", color="black", weight=3]; 6136[label="absReal1 (Pos (Succ vuz1440)) True",fontsize=16,color="black",shape="box"];6136 -> 6144[label="",style="solid", color="black", weight=3]; 6137[label="Pos Zero",fontsize=16,color="green",shape="box"];6138[label="primRemInt (Pos vuz3740) (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6138 -> 6145[label="",style="solid", color="black", weight=3]; 6139[label="primRemInt (Neg vuz3740) (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6139 -> 6146[label="",style="solid", color="black", weight=3]; 6140[label="primRemInt (Pos vuz3740) (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6140 -> 6147[label="",style="solid", color="black", weight=3]; 6141[label="primRemInt (Neg vuz3740) (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6141 -> 6148[label="",style="solid", color="black", weight=3]; 6142[label="Neg Zero",fontsize=16,color="green",shape="box"];6143[label="`negate` Neg (Succ vuz2820)",fontsize=16,color="black",shape="box"];6143 -> 6149[label="",style="solid", color="black", weight=3]; 6144[label="Pos (Succ vuz1440)",fontsize=16,color="green",shape="box"];6145[label="Pos (primModNatS vuz3740 (Succ vuz37300))",fontsize=16,color="green",shape="box"];6145 -> 6150[label="",style="dashed", color="green", weight=3]; 6146[label="Neg (primModNatS vuz3740 (Succ vuz37300))",fontsize=16,color="green",shape="box"];6146 -> 6151[label="",style="dashed", color="green", weight=3]; 6147[label="Pos (primModNatS vuz3740 (Succ vuz37300))",fontsize=16,color="green",shape="box"];6147 -> 6152[label="",style="dashed", color="green", weight=3]; 6148[label="Neg (primModNatS vuz3740 (Succ vuz37300))",fontsize=16,color="green",shape="box"];6148 -> 6153[label="",style="dashed", color="green", weight=3]; 6149[label="primNegInt (Neg (Succ vuz2820))",fontsize=16,color="black",shape="box"];6149 -> 6154[label="",style="solid", color="black", weight=3]; 6150[label="primModNatS vuz3740 (Succ vuz37300)",fontsize=16,color="burlywood",shape="triangle"];6590[label="vuz3740/Succ vuz37400",fontsize=10,color="white",style="solid",shape="box"];6150 -> 6590[label="",style="solid", color="burlywood", weight=9]; 6590 -> 6155[label="",style="solid", color="burlywood", weight=3]; 6591[label="vuz3740/Zero",fontsize=10,color="white",style="solid",shape="box"];6150 -> 6591[label="",style="solid", color="burlywood", weight=9]; 6591 -> 6156[label="",style="solid", color="burlywood", weight=3]; 6151 -> 6150[label="",style="dashed", color="red", weight=0]; 6151[label="primModNatS vuz3740 (Succ vuz37300)",fontsize=16,color="magenta"];6151 -> 6157[label="",style="dashed", color="magenta", weight=3]; 6152 -> 6150[label="",style="dashed", color="red", weight=0]; 6152[label="primModNatS vuz3740 (Succ vuz37300)",fontsize=16,color="magenta"];6152 -> 6158[label="",style="dashed", color="magenta", weight=3]; 6153 -> 6150[label="",style="dashed", color="red", weight=0]; 6153[label="primModNatS vuz3740 (Succ vuz37300)",fontsize=16,color="magenta"];6153 -> 6159[label="",style="dashed", color="magenta", weight=3]; 6153 -> 6160[label="",style="dashed", color="magenta", weight=3]; 6154[label="Pos (Succ vuz2820)",fontsize=16,color="green",shape="box"];6155[label="primModNatS (Succ vuz37400) (Succ vuz37300)",fontsize=16,color="black",shape="box"];6155 -> 6161[label="",style="solid", color="black", weight=3]; 6156[label="primModNatS Zero (Succ vuz37300)",fontsize=16,color="black",shape="box"];6156 -> 6162[label="",style="solid", color="black", weight=3]; 6157[label="vuz3740",fontsize=16,color="green",shape="box"];6158[label="vuz37300",fontsize=16,color="green",shape="box"];6159[label="vuz3740",fontsize=16,color="green",shape="box"];6160[label="vuz37300",fontsize=16,color="green",shape="box"];6161[label="primModNatS0 vuz37400 vuz37300 (primGEqNatS vuz37400 vuz37300)",fontsize=16,color="burlywood",shape="box"];6592[label="vuz37400/Succ vuz374000",fontsize=10,color="white",style="solid",shape="box"];6161 -> 6592[label="",style="solid", color="burlywood", weight=9]; 6592 -> 6163[label="",style="solid", color="burlywood", weight=3]; 6593[label="vuz37400/Zero",fontsize=10,color="white",style="solid",shape="box"];6161 -> 6593[label="",style="solid", color="burlywood", weight=9]; 6593 -> 6164[label="",style="solid", color="burlywood", weight=3]; 6162[label="Zero",fontsize=16,color="green",shape="box"];6163[label="primModNatS0 (Succ vuz374000) vuz37300 (primGEqNatS (Succ vuz374000) vuz37300)",fontsize=16,color="burlywood",shape="box"];6594[label="vuz37300/Succ vuz373000",fontsize=10,color="white",style="solid",shape="box"];6163 -> 6594[label="",style="solid", color="burlywood", weight=9]; 6594 -> 6165[label="",style="solid", color="burlywood", weight=3]; 6595[label="vuz37300/Zero",fontsize=10,color="white",style="solid",shape="box"];6163 -> 6595[label="",style="solid", color="burlywood", weight=9]; 6595 -> 6166[label="",style="solid", color="burlywood", weight=3]; 6164[label="primModNatS0 Zero vuz37300 (primGEqNatS Zero vuz37300)",fontsize=16,color="burlywood",shape="box"];6596[label="vuz37300/Succ vuz373000",fontsize=10,color="white",style="solid",shape="box"];6164 -> 6596[label="",style="solid", color="burlywood", weight=9]; 6596 -> 6167[label="",style="solid", color="burlywood", weight=3]; 6597[label="vuz37300/Zero",fontsize=10,color="white",style="solid",shape="box"];6164 -> 6597[label="",style="solid", color="burlywood", weight=9]; 6597 -> 6168[label="",style="solid", color="burlywood", weight=3]; 6165[label="primModNatS0 (Succ vuz374000) (Succ vuz373000) (primGEqNatS (Succ vuz374000) (Succ vuz373000))",fontsize=16,color="black",shape="box"];6165 -> 6169[label="",style="solid", color="black", weight=3]; 6166[label="primModNatS0 (Succ vuz374000) Zero (primGEqNatS (Succ vuz374000) Zero)",fontsize=16,color="black",shape="box"];6166 -> 6170[label="",style="solid", color="black", weight=3]; 6167[label="primModNatS0 Zero (Succ vuz373000) (primGEqNatS Zero (Succ vuz373000))",fontsize=16,color="black",shape="box"];6167 -> 6171[label="",style="solid", color="black", weight=3]; 6168[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];6168 -> 6172[label="",style="solid", color="black", weight=3]; 6169 -> 6331[label="",style="dashed", color="red", weight=0]; 6169[label="primModNatS0 (Succ vuz374000) (Succ vuz373000) (primGEqNatS vuz374000 vuz373000)",fontsize=16,color="magenta"];6169 -> 6332[label="",style="dashed", color="magenta", weight=3]; 6169 -> 6333[label="",style="dashed", color="magenta", weight=3]; 6169 -> 6334[label="",style="dashed", color="magenta", weight=3]; 6169 -> 6335[label="",style="dashed", color="magenta", weight=3]; 6170[label="primModNatS0 (Succ vuz374000) Zero True",fontsize=16,color="black",shape="box"];6170 -> 6175[label="",style="solid", color="black", weight=3]; 6171[label="primModNatS0 Zero (Succ vuz373000) False",fontsize=16,color="black",shape="box"];6171 -> 6176[label="",style="solid", color="black", weight=3]; 6172[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];6172 -> 6177[label="",style="solid", color="black", weight=3]; 6332[label="vuz373000",fontsize=16,color="green",shape="box"];6333[label="vuz373000",fontsize=16,color="green",shape="box"];6334[label="vuz374000",fontsize=16,color="green",shape="box"];6335[label="vuz374000",fontsize=16,color="green",shape="box"];6331[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS vuz393 vuz394)",fontsize=16,color="burlywood",shape="triangle"];6598[label="vuz393/Succ vuz3930",fontsize=10,color="white",style="solid",shape="box"];6331 -> 6598[label="",style="solid", color="burlywood", weight=9]; 6598 -> 6364[label="",style="solid", color="burlywood", weight=3]; 6599[label="vuz393/Zero",fontsize=10,color="white",style="solid",shape="box"];6331 -> 6599[label="",style="solid", color="burlywood", weight=9]; 6599 -> 6365[label="",style="solid", color="burlywood", weight=3]; 6175 -> 6150[label="",style="dashed", color="red", weight=0]; 6175[label="primModNatS (primMinusNatS (Succ vuz374000) Zero) (Succ Zero)",fontsize=16,color="magenta"];6175 -> 6182[label="",style="dashed", color="magenta", weight=3]; 6175 -> 6183[label="",style="dashed", color="magenta", weight=3]; 6176[label="Succ Zero",fontsize=16,color="green",shape="box"];6177 -> 6150[label="",style="dashed", color="red", weight=0]; 6177[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];6177 -> 6184[label="",style="dashed", color="magenta", weight=3]; 6177 -> 6185[label="",style="dashed", color="magenta", weight=3]; 6364[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS (Succ vuz3930) vuz394)",fontsize=16,color="burlywood",shape="box"];6600[label="vuz394/Succ vuz3940",fontsize=10,color="white",style="solid",shape="box"];6364 -> 6600[label="",style="solid", color="burlywood", weight=9]; 6600 -> 6366[label="",style="solid", color="burlywood", weight=3]; 6601[label="vuz394/Zero",fontsize=10,color="white",style="solid",shape="box"];6364 -> 6601[label="",style="solid", color="burlywood", weight=9]; 6601 -> 6367[label="",style="solid", color="burlywood", weight=3]; 6365[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS Zero vuz394)",fontsize=16,color="burlywood",shape="box"];6602[label="vuz394/Succ vuz3940",fontsize=10,color="white",style="solid",shape="box"];6365 -> 6602[label="",style="solid", color="burlywood", weight=9]; 6602 -> 6368[label="",style="solid", color="burlywood", weight=3]; 6603[label="vuz394/Zero",fontsize=10,color="white",style="solid",shape="box"];6365 -> 6603[label="",style="solid", color="burlywood", weight=9]; 6603 -> 6369[label="",style="solid", color="burlywood", weight=3]; 6182 -> 5741[label="",style="dashed", color="red", weight=0]; 6182[label="primMinusNatS (Succ vuz374000) Zero",fontsize=16,color="magenta"];6182 -> 6190[label="",style="dashed", color="magenta", weight=3]; 6182 -> 6191[label="",style="dashed", color="magenta", weight=3]; 6183[label="Zero",fontsize=16,color="green",shape="box"];6184 -> 5741[label="",style="dashed", color="red", weight=0]; 6184[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];6184 -> 6192[label="",style="dashed", color="magenta", weight=3]; 6184 -> 6193[label="",style="dashed", color="magenta", weight=3]; 6185[label="Zero",fontsize=16,color="green",shape="box"];6366[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS (Succ vuz3930) (Succ vuz3940))",fontsize=16,color="black",shape="box"];6366 -> 6370[label="",style="solid", color="black", weight=3]; 6367[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS (Succ vuz3930) Zero)",fontsize=16,color="black",shape="box"];6367 -> 6371[label="",style="solid", color="black", weight=3]; 6368[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS Zero (Succ vuz3940))",fontsize=16,color="black",shape="box"];6368 -> 6372[label="",style="solid", color="black", weight=3]; 6369[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];6369 -> 6373[label="",style="solid", color="black", weight=3]; 6190[label="Succ vuz374000",fontsize=16,color="green",shape="box"];6191[label="Zero",fontsize=16,color="green",shape="box"];6192[label="Zero",fontsize=16,color="green",shape="box"];6193[label="Zero",fontsize=16,color="green",shape="box"];6370 -> 6331[label="",style="dashed", color="red", weight=0]; 6370[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS vuz3930 vuz3940)",fontsize=16,color="magenta"];6370 -> 6374[label="",style="dashed", color="magenta", weight=3]; 6370 -> 6375[label="",style="dashed", color="magenta", weight=3]; 6371[label="primModNatS0 (Succ vuz391) (Succ vuz392) True",fontsize=16,color="black",shape="triangle"];6371 -> 6376[label="",style="solid", color="black", weight=3]; 6372[label="primModNatS0 (Succ vuz391) (Succ vuz392) False",fontsize=16,color="black",shape="box"];6372 -> 6377[label="",style="solid", color="black", weight=3]; 6373 -> 6371[label="",style="dashed", color="red", weight=0]; 6373[label="primModNatS0 (Succ vuz391) (Succ vuz392) True",fontsize=16,color="magenta"];6374[label="vuz3940",fontsize=16,color="green",shape="box"];6375[label="vuz3930",fontsize=16,color="green",shape="box"];6376 -> 6150[label="",style="dashed", color="red", weight=0]; 6376[label="primModNatS (primMinusNatS (Succ vuz391) (Succ vuz392)) (Succ (Succ vuz392))",fontsize=16,color="magenta"];6376 -> 6378[label="",style="dashed", color="magenta", weight=3]; 6376 -> 6379[label="",style="dashed", color="magenta", weight=3]; 6377[label="Succ (Succ vuz391)",fontsize=16,color="green",shape="box"];6378 -> 5741[label="",style="dashed", color="red", weight=0]; 6378[label="primMinusNatS (Succ vuz391) (Succ vuz392)",fontsize=16,color="magenta"];6378 -> 6380[label="",style="dashed", color="magenta", weight=3]; 6378 -> 6381[label="",style="dashed", color="magenta", weight=3]; 6379[label="Succ vuz392",fontsize=16,color="green",shape="box"];6380[label="Succ vuz391",fontsize=16,color="green",shape="box"];6381[label="Succ vuz392",fontsize=16,color="green",shape="box"];} ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(vuz374, Pos(Succ(vuz37300))) -> new_gcd0Gcd'(Pos(Succ(vuz37300)), new_primRemInt(vuz374, vuz37300)) new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) The TRS R consists of the following rules: new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primRemInt(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Zero, vuz37300) -> Zero new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primRemInt(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primRemInt(Pos(x0), x1) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primRemInt(Neg(x0), x1) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primRemInt0(Pos(x0), x1) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (14) MNOCProof (EQUIVALENT) We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. ---------------------------------------- (15) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(vuz374, Pos(Succ(vuz37300))) -> new_gcd0Gcd'(Pos(Succ(vuz37300)), new_primRemInt(vuz374, vuz37300)) new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) The TRS R consists of the following rules: new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primRemInt(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Zero, vuz37300) -> Zero new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primRemInt(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (16) InductionCalculusProof (EQUIVALENT) Note that final constraints are written in bold face. For Pair new_gcd0Gcd'(vuz374, Pos(Succ(vuz37300))) -> new_gcd0Gcd'(Pos(Succ(vuz37300)), new_primRemInt(vuz374, vuz37300)) the following chains were created: *We consider the chain new_gcd0Gcd'(x0, Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), new_primRemInt(x0, x1)), new_gcd0Gcd'(x2, Pos(Succ(x3))) -> new_gcd0Gcd'(Pos(Succ(x3)), new_primRemInt(x2, x3)) which results in the following constraint: (1) (new_gcd0Gcd'(Pos(Succ(x1)), new_primRemInt(x0, x1))=new_gcd0Gcd'(x2, Pos(Succ(x3))) ==> new_gcd0Gcd'(x0, Pos(Succ(x1)))_>=_new_gcd0Gcd'(Pos(Succ(x1)), new_primRemInt(x0, x1))) We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint: (2) (new_primRemInt(x0, x1)=Pos(Succ(x3)) ==> new_gcd0Gcd'(x0, Pos(Succ(x1)))_>=_new_gcd0Gcd'(Pos(Succ(x1)), new_primRemInt(x0, x1))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primRemInt(x0, x1)=Pos(Succ(x3)) which results in the following new constraint: (3) (Pos(new_primModNatS1(x17, x16))=Pos(Succ(x3)) ==> new_gcd0Gcd'(Pos(x17), Pos(Succ(x16)))_>=_new_gcd0Gcd'(Pos(Succ(x16)), new_primRemInt(Pos(x17), x16))) We simplified constraint (3) using rules (I), (II) which results in the following new constraint: (4) (new_primModNatS1(x17, x16)=Succ(x3) ==> new_gcd0Gcd'(Pos(x17), Pos(Succ(x16)))_>=_new_gcd0Gcd'(Pos(Succ(x16)), new_primRemInt(Pos(x17), x16))) We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS1(x17, x16)=Succ(x3) which results in the following new constraints: (5) (Succ(Zero)=Succ(x3) ==> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x20))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x20))), new_primRemInt(Pos(Succ(Zero)), Succ(x20)))) (6) (new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)=Succ(x3) ==> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Pos(Succ(Zero)), Zero))) (7) (new_primModNatS1(new_primMinusNatS0(Succ(x21), Zero), Zero)=Succ(x3) ==> new_gcd0Gcd'(Pos(Succ(Succ(x21))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Pos(Succ(Succ(x21))), Zero))) (8) (new_primModNatS01(x23, x22, x23, x22)=Succ(x3) ==> new_gcd0Gcd'(Pos(Succ(Succ(x23))), Pos(Succ(Succ(x22))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x22))), new_primRemInt(Pos(Succ(Succ(x23))), Succ(x22)))) We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint: (9) (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x20))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x20))), new_primRemInt(Pos(Succ(Zero)), Succ(x20)))) We simplified constraint (6) using rules (III), (IV), (VII) which results in the following new constraint: (10) (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Pos(Succ(Zero)), Zero))) We simplified constraint (7) using rules (III), (IV), (VII) which results in the following new constraint: (11) (new_gcd0Gcd'(Pos(Succ(Succ(x21))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Pos(Succ(Succ(x21))), Zero))) We simplified constraint (8) using rules (III), (IV), (VII) which results in the following new constraint: (12) (new_gcd0Gcd'(Pos(Succ(Succ(x33))), Pos(Succ(Succ(x34))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x34))), new_primRemInt(Pos(Succ(Succ(x33))), Succ(x34)))) *We consider the chain new_gcd0Gcd'(x4, Pos(Succ(x5))) -> new_gcd0Gcd'(Pos(Succ(x5)), new_primRemInt(x4, x5)), new_gcd0Gcd'(x6, Neg(Succ(x7))) -> new_gcd0Gcd'(Neg(Succ(x7)), new_primRemInt0(x6, x7)) which results in the following constraint: (1) (new_gcd0Gcd'(Pos(Succ(x5)), new_primRemInt(x4, x5))=new_gcd0Gcd'(x6, Neg(Succ(x7))) ==> new_gcd0Gcd'(x4, Pos(Succ(x5)))_>=_new_gcd0Gcd'(Pos(Succ(x5)), new_primRemInt(x4, x5))) We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint: (2) (new_primRemInt(x4, x5)=Neg(Succ(x7)) ==> new_gcd0Gcd'(x4, Pos(Succ(x5)))_>=_new_gcd0Gcd'(Pos(Succ(x5)), new_primRemInt(x4, x5))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primRemInt(x4, x5)=Neg(Succ(x7)) which results in the following new constraint: (3) (Neg(new_primModNatS1(x38, x37))=Neg(Succ(x7)) ==> new_gcd0Gcd'(Neg(x38), Pos(Succ(x37)))_>=_new_gcd0Gcd'(Pos(Succ(x37)), new_primRemInt(Neg(x38), x37))) We simplified constraint (3) using rules (I), (II) which results in the following new constraint: (4) (new_primModNatS1(x38, x37)=Succ(x7) ==> new_gcd0Gcd'(Neg(x38), Pos(Succ(x37)))_>=_new_gcd0Gcd'(Pos(Succ(x37)), new_primRemInt(Neg(x38), x37))) We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS1(x38, x37)=Succ(x7) which results in the following new constraints: (5) (Succ(Zero)=Succ(x7) ==> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x39))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x39))), new_primRemInt(Neg(Succ(Zero)), Succ(x39)))) (6) (new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)=Succ(x7) ==> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Neg(Succ(Zero)), Zero))) (7) (new_primModNatS1(new_primMinusNatS0(Succ(x40), Zero), Zero)=Succ(x7) ==> new_gcd0Gcd'(Neg(Succ(Succ(x40))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Neg(Succ(Succ(x40))), Zero))) (8) (new_primModNatS01(x42, x41, x42, x41)=Succ(x7) ==> new_gcd0Gcd'(Neg(Succ(Succ(x42))), Pos(Succ(Succ(x41))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x41))), new_primRemInt(Neg(Succ(Succ(x42))), Succ(x41)))) We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint: (9) (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x39))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x39))), new_primRemInt(Neg(Succ(Zero)), Succ(x39)))) We simplified constraint (6) using rules (III), (IV), (VII) which results in the following new constraint: (10) (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Neg(Succ(Zero)), Zero))) We simplified constraint (7) using rules (III), (IV), (VII) which results in the following new constraint: (11) (new_gcd0Gcd'(Neg(Succ(Succ(x40))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Neg(Succ(Succ(x40))), Zero))) We simplified constraint (8) using rules (III), (IV), (VII) which results in the following new constraint: (12) (new_gcd0Gcd'(Neg(Succ(Succ(x52))), Pos(Succ(Succ(x53))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x53))), new_primRemInt(Neg(Succ(Succ(x52))), Succ(x53)))) For Pair new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) the following chains were created: *We consider the chain new_gcd0Gcd'(x8, Neg(Succ(x9))) -> new_gcd0Gcd'(Neg(Succ(x9)), new_primRemInt0(x8, x9)), new_gcd0Gcd'(x10, Pos(Succ(x11))) -> new_gcd0Gcd'(Pos(Succ(x11)), new_primRemInt(x10, x11)) which results in the following constraint: (1) (new_gcd0Gcd'(Neg(Succ(x9)), new_primRemInt0(x8, x9))=new_gcd0Gcd'(x10, Pos(Succ(x11))) ==> new_gcd0Gcd'(x8, Neg(Succ(x9)))_>=_new_gcd0Gcd'(Neg(Succ(x9)), new_primRemInt0(x8, x9))) We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint: (2) (new_primRemInt0(x8, x9)=Pos(Succ(x11)) ==> new_gcd0Gcd'(x8, Neg(Succ(x9)))_>=_new_gcd0Gcd'(Neg(Succ(x9)), new_primRemInt0(x8, x9))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primRemInt0(x8, x9)=Pos(Succ(x11)) which results in the following new constraint: (3) (Pos(new_primModNatS1(x57, x56))=Pos(Succ(x11)) ==> new_gcd0Gcd'(Pos(x57), Neg(Succ(x56)))_>=_new_gcd0Gcd'(Neg(Succ(x56)), new_primRemInt0(Pos(x57), x56))) We simplified constraint (3) using rules (I), (II) which results in the following new constraint: (4) (new_primModNatS1(x57, x56)=Succ(x11) ==> new_gcd0Gcd'(Pos(x57), Neg(Succ(x56)))_>=_new_gcd0Gcd'(Neg(Succ(x56)), new_primRemInt0(Pos(x57), x56))) We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS1(x57, x56)=Succ(x11) which results in the following new constraints: (5) (Succ(Zero)=Succ(x11) ==> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x58))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x58))), new_primRemInt0(Pos(Succ(Zero)), Succ(x58)))) (6) (new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)=Succ(x11) ==> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Pos(Succ(Zero)), Zero))) (7) (new_primModNatS1(new_primMinusNatS0(Succ(x59), Zero), Zero)=Succ(x11) ==> new_gcd0Gcd'(Pos(Succ(Succ(x59))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Pos(Succ(Succ(x59))), Zero))) (8) (new_primModNatS01(x61, x60, x61, x60)=Succ(x11) ==> new_gcd0Gcd'(Pos(Succ(Succ(x61))), Neg(Succ(Succ(x60))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x60))), new_primRemInt0(Pos(Succ(Succ(x61))), Succ(x60)))) We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint: (9) (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x58))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x58))), new_primRemInt0(Pos(Succ(Zero)), Succ(x58)))) We simplified constraint (6) using rules (III), (IV), (VII) which results in the following new constraint: (10) (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Pos(Succ(Zero)), Zero))) We simplified constraint (7) using rules (III), (IV), (VII) which results in the following new constraint: (11) (new_gcd0Gcd'(Pos(Succ(Succ(x59))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Pos(Succ(Succ(x59))), Zero))) We simplified constraint (8) using rules (III), (IV), (VII) which results in the following new constraint: (12) (new_gcd0Gcd'(Pos(Succ(Succ(x71))), Neg(Succ(Succ(x72))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x72))), new_primRemInt0(Pos(Succ(Succ(x71))), Succ(x72)))) *We consider the chain new_gcd0Gcd'(x12, Neg(Succ(x13))) -> new_gcd0Gcd'(Neg(Succ(x13)), new_primRemInt0(x12, x13)), new_gcd0Gcd'(x14, Neg(Succ(x15))) -> new_gcd0Gcd'(Neg(Succ(x15)), new_primRemInt0(x14, x15)) which results in the following constraint: (1) (new_gcd0Gcd'(Neg(Succ(x13)), new_primRemInt0(x12, x13))=new_gcd0Gcd'(x14, Neg(Succ(x15))) ==> new_gcd0Gcd'(x12, Neg(Succ(x13)))_>=_new_gcd0Gcd'(Neg(Succ(x13)), new_primRemInt0(x12, x13))) We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint: (2) (new_primRemInt0(x12, x13)=Neg(Succ(x15)) ==> new_gcd0Gcd'(x12, Neg(Succ(x13)))_>=_new_gcd0Gcd'(Neg(Succ(x13)), new_primRemInt0(x12, x13))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primRemInt0(x12, x13)=Neg(Succ(x15)) which results in the following new constraint: (3) (Neg(new_primModNatS1(x74, x73))=Neg(Succ(x15)) ==> new_gcd0Gcd'(Neg(x74), Neg(Succ(x73)))_>=_new_gcd0Gcd'(Neg(Succ(x73)), new_primRemInt0(Neg(x74), x73))) We simplified constraint (3) using rules (I), (II) which results in the following new constraint: (4) (new_primModNatS1(x74, x73)=Succ(x15) ==> new_gcd0Gcd'(Neg(x74), Neg(Succ(x73)))_>=_new_gcd0Gcd'(Neg(Succ(x73)), new_primRemInt0(Neg(x74), x73))) We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS1(x74, x73)=Succ(x15) which results in the following new constraints: (5) (Succ(Zero)=Succ(x15) ==> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x77))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x77))), new_primRemInt0(Neg(Succ(Zero)), Succ(x77)))) (6) (new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)=Succ(x15) ==> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Neg(Succ(Zero)), Zero))) (7) (new_primModNatS1(new_primMinusNatS0(Succ(x78), Zero), Zero)=Succ(x15) ==> new_gcd0Gcd'(Neg(Succ(Succ(x78))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Neg(Succ(Succ(x78))), Zero))) (8) (new_primModNatS01(x80, x79, x80, x79)=Succ(x15) ==> new_gcd0Gcd'(Neg(Succ(Succ(x80))), Neg(Succ(Succ(x79))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x79))), new_primRemInt0(Neg(Succ(Succ(x80))), Succ(x79)))) We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint: (9) (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x77))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x77))), new_primRemInt0(Neg(Succ(Zero)), Succ(x77)))) We simplified constraint (6) using rules (III), (IV), (VII) which results in the following new constraint: (10) (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Neg(Succ(Zero)), Zero))) We simplified constraint (7) using rules (III), (IV), (VII) which results in the following new constraint: (11) (new_gcd0Gcd'(Neg(Succ(Succ(x78))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Neg(Succ(Succ(x78))), Zero))) We simplified constraint (8) using rules (III), (IV), (VII) which results in the following new constraint: (12) (new_gcd0Gcd'(Neg(Succ(Succ(x90))), Neg(Succ(Succ(x91))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x91))), new_primRemInt0(Neg(Succ(Succ(x90))), Succ(x91)))) To summarize, we get the following constraints P__>=_ for the following pairs. *new_gcd0Gcd'(vuz374, Pos(Succ(vuz37300))) -> new_gcd0Gcd'(Pos(Succ(vuz37300)), new_primRemInt(vuz374, vuz37300)) *(new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x20))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x20))), new_primRemInt(Pos(Succ(Zero)), Succ(x20)))) *(new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Pos(Succ(Zero)), Zero))) *(new_gcd0Gcd'(Pos(Succ(Succ(x21))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Pos(Succ(Succ(x21))), Zero))) *(new_gcd0Gcd'(Pos(Succ(Succ(x33))), Pos(Succ(Succ(x34))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x34))), new_primRemInt(Pos(Succ(Succ(x33))), Succ(x34)))) *(new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x39))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x39))), new_primRemInt(Neg(Succ(Zero)), Succ(x39)))) *(new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Neg(Succ(Zero)), Zero))) *(new_gcd0Gcd'(Neg(Succ(Succ(x40))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Neg(Succ(Succ(x40))), Zero))) *(new_gcd0Gcd'(Neg(Succ(Succ(x52))), Pos(Succ(Succ(x53))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x53))), new_primRemInt(Neg(Succ(Succ(x52))), Succ(x53)))) *new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) *(new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x58))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x58))), new_primRemInt0(Pos(Succ(Zero)), Succ(x58)))) *(new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Pos(Succ(Zero)), Zero))) *(new_gcd0Gcd'(Pos(Succ(Succ(x59))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Pos(Succ(Succ(x59))), Zero))) *(new_gcd0Gcd'(Pos(Succ(Succ(x71))), Neg(Succ(Succ(x72))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x72))), new_primRemInt0(Pos(Succ(Succ(x71))), Succ(x72)))) *(new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x77))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x77))), new_primRemInt0(Neg(Succ(Zero)), Succ(x77)))) *(new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Neg(Succ(Zero)), Zero))) *(new_gcd0Gcd'(Neg(Succ(Succ(x78))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Neg(Succ(Succ(x78))), Zero))) *(new_gcd0Gcd'(Neg(Succ(Succ(x90))), Neg(Succ(Succ(x91))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x91))), new_primRemInt0(Neg(Succ(Succ(x90))), Succ(x91)))) The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. ---------------------------------------- (17) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(vuz374, Pos(Succ(vuz37300))) -> new_gcd0Gcd'(Pos(Succ(vuz37300)), new_primRemInt(vuz374, vuz37300)) new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) The TRS R consists of the following rules: new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primRemInt(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Zero, vuz37300) -> Zero new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primRemInt(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primRemInt(Pos(x0), x1) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primRemInt(Neg(x0), x1) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primRemInt0(Pos(x0), x1) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (18) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(vuz374, Pos(Succ(vuz37300))) -> new_gcd0Gcd'(Pos(Succ(vuz37300)), new_primRemInt(vuz374, vuz37300)) at position [1] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1))),new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1)))) (new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))),new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1)))) ---------------------------------------- (19) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primRemInt(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Zero, vuz37300) -> Zero new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primRemInt(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primRemInt(Pos(x0), x1) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primRemInt(Neg(x0), x1) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primRemInt0(Pos(x0), x1) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (20) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. ---------------------------------------- (21) Complex Obligation (AND) ---------------------------------------- (22) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primRemInt(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Zero, vuz37300) -> Zero new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primRemInt(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primRemInt(Pos(x0), x1) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primRemInt(Neg(x0), x1) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primRemInt0(Pos(x0), x1) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (23) UsableRulesProof (EQUIVALENT) As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (24) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primRemInt(Pos(x0), x1) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primRemInt(Neg(x0), x1) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primRemInt0(Pos(x0), x1) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (25) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. new_primRemInt(Pos(x0), x1) new_primRemInt0(Neg(x0), x1) new_primRemInt(Neg(x0), x1) new_primRemInt0(Pos(x0), x1) ---------------------------------------- (26) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (27) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(new_primModNatS01(x0, x1, x0, x1))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(new_primModNatS01(x0, x1, x0, x1)))) (new_gcd0Gcd'(Pos(Zero), Pos(Succ(x0))) -> new_gcd0Gcd'(Pos(Succ(x0)), Pos(Zero)),new_gcd0Gcd'(Pos(Zero), Pos(Succ(x0))) -> new_gcd0Gcd'(Pos(Succ(x0)), Pos(Zero))) ---------------------------------------- (28) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Zero), Pos(Succ(x0))) -> new_gcd0Gcd'(Pos(Succ(x0)), Pos(Zero)) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (29) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node. ---------------------------------------- (30) Complex Obligation (AND) ---------------------------------------- (31) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (32) UsableRulesProof (EQUIVALENT) As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (33) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (34) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. new_primModNatS02(x0, x1) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) ---------------------------------------- (35) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (36) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (37) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (38) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (39) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (40) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (41) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (42) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) ---------------------------------------- (43) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (44) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (45) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (46) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (47) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (48) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (49) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (50) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) ---------------------------------------- (51) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (52) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (53) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (54) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (55) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (56) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (57) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (58) QDPSizeChangeProof (EQUIVALENT) We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. Order:Polynomial interpretation [POLO]: POL(Pos(x_1)) = x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 1 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 From the DPs we obtained the following set of size-change graphs: *new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 2 >= 1, 1 > 2 *new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 2 >= 1, 1 >= 2 We oriented the following set of usable rules [AAECC05,FROCOS05]. new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (59) YES ---------------------------------------- (60) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(new_primModNatS01(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (61) UsableRulesProof (EQUIVALENT) As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (62) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(new_primModNatS01(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (63) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(new_primModNatS01(x0, x1, x0, x1))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS02(Zero, Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS02(Zero, Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS02(Succ(x2), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS02(Succ(x2), Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))) ---------------------------------------- (64) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS02(Zero, Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS02(Succ(x2), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (65) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. ---------------------------------------- (66) Complex Obligation (AND) ---------------------------------------- (67) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS02(Zero, Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS02(Succ(x2), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (68) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS02(Zero, Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero))))) ---------------------------------------- (69) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS02(Succ(x2), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (70) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS02(Succ(x2), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero))))) ---------------------------------------- (71) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (72) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero))))) ---------------------------------------- (73) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (74) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero))))) ---------------------------------------- (75) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (76) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(Zero, Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(Zero, Succ(Zero))))) ---------------------------------------- (77) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(Zero, Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (78) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (79) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (80) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero))))) ---------------------------------------- (81) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (82) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS01(x0, Zero, x0, Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS01(x0, Zero, x0, Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero)))) ---------------------------------------- (83) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS01(x0, Zero, x0, Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (84) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (85) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS01(x0, Zero, x0, Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (86) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS01(x0, Zero, x0, Zero))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Pos(x_1)) = 2*x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_gcd0Gcd'(x_1, x_2)) = 2*x_1 + 2*x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS01(x_1, x_2, x_3, x_4)) = 3 + x_1 POL(new_primModNatS02(x_1, x_2)) = 3 + x_1 POL(new_primModNatS1(x_1, x_2)) = 2 + x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (87) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (88) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (89) TRUE ---------------------------------------- (90) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (91) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Zero), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Zero), Succ(Zero))))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero))))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))) ---------------------------------------- (92) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Zero), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (93) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. ---------------------------------------- (94) Complex Obligation (AND) ---------------------------------------- (95) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Zero), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (96) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Zero), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero)))))) ---------------------------------------- (97) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (98) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero)))))) ---------------------------------------- (99) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (100) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero)))))) ---------------------------------------- (101) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (102) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero)))))) ---------------------------------------- (103) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (104) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero)))))) ---------------------------------------- (105) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (106) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero)))))) ---------------------------------------- (107) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (108) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Zero, Succ(Succ(Zero)))))) ---------------------------------------- (109) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (110) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (111) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (112) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero)))))) ---------------------------------------- (113) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (114) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Pos(x_1)) = 2*x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_gcd0Gcd'(x_1, x_2)) = 2*x_1 + 2*x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS01(x_1, x_2, x_3, x_4)) = 2 + x_1 POL(new_primModNatS02(x_1, x_2)) = 1 + x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (115) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (116) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (117) TRUE ---------------------------------------- (118) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (119) InductionCalculusProof (EQUIVALENT) Note that final constraints are written in bold face. For Pair new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) the following chains were created: *We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Succ(Succ(x1)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x1))))), Pos(new_primModNatS01(Succ(Succ(x0)), Succ(Succ(x1)), x0, x1))), new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) which results in the following constraint: (1) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x1))))), Pos(new_primModNatS01(Succ(Succ(x0)), Succ(Succ(x1)), x0, x1)))=new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Succ(Succ(x1))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x1))))), Pos(new_primModNatS01(Succ(Succ(x0)), Succ(Succ(x1)), x0, x1)))) We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint: (2) (Succ(Succ(x0))=x4 & Succ(Succ(x1))=x5 & new_primModNatS01(x4, x5, x0, x1)=Succ(Succ(Succ(Succ(x3)))) ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Succ(Succ(x1))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x1))))), Pos(new_primModNatS01(Succ(Succ(x0)), Succ(Succ(x1)), x0, x1)))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x4, x5, x0, x1)=Succ(Succ(Succ(Succ(x3)))) which results in the following new constraints: (3) (new_primModNatS02(x7, x6)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Zero))=x7 & Succ(Succ(Zero))=x6 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) (4) (new_primModNatS01(x11, x10, x9, x8)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(x9)))=x11 & Succ(Succ(Succ(x8)))=x10 & (\/x12:new_primModNatS01(x11, x10, x9, x8)=Succ(Succ(Succ(Succ(x12)))) & Succ(Succ(x9))=x11 & Succ(Succ(x8))=x10 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x9))))), Pos(Succ(Succ(Succ(Succ(x8))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x8))))), Pos(new_primModNatS01(Succ(Succ(x9)), Succ(Succ(x8)), x9, x8)))) ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x9)))))), Pos(Succ(Succ(Succ(Succ(Succ(x8)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x8)))))), Pos(new_primModNatS01(Succ(Succ(Succ(x9))), Succ(Succ(Succ(x8))), Succ(x9), Succ(x8))))) (5) (new_primModNatS02(x15, x14)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(x13)))=x15 & Succ(Succ(Zero))=x14 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x13)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS01(Succ(Succ(Succ(x13))), Succ(Succ(Zero)), Succ(x13), Zero)))) (6) (Succ(Succ(x18))=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Zero))=x18 & Succ(Succ(Succ(x16)))=x17 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x16)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x16)))))), Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x16))), Zero, Succ(x16))))) We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x7, x6)=Succ(Succ(Succ(Succ(x3)))) which results in the following new constraint: (7) (new_primModNatS1(new_primMinusNatS0(Succ(x20), Succ(x19)), Succ(x19))=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Zero))=x20 & Succ(Succ(Zero))=x19 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) We simplified constraint (4) using rule (IV) which results in the following new constraint: (8) (new_primModNatS01(x11, x10, x9, x8)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(x9)))=x11 & Succ(Succ(Succ(x8)))=x10 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x9)))))), Pos(Succ(Succ(Succ(Succ(Succ(x8)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x8)))))), Pos(new_primModNatS01(Succ(Succ(Succ(x9))), Succ(Succ(Succ(x8))), Succ(x9), Succ(x8))))) We simplified constraint (5) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x15, x14)=Succ(Succ(Succ(Succ(x3)))) which results in the following new constraint: (9) (new_primModNatS1(new_primMinusNatS0(Succ(x39), Succ(x38)), Succ(x38))=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(x13)))=x39 & Succ(Succ(Zero))=x38 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x13)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS01(Succ(Succ(Succ(x13))), Succ(Succ(Zero)), Succ(x13), Zero)))) We simplified constraint (6) using rules (I), (II), (III), (IV) which results in the following new constraint: (10) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x16)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x16)))))), Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x16))), Zero, Succ(x16))))) We simplified constraint (7) using rules (III), (IV), (VII) which results in the following new constraint: (11) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x11, x10, x9, x8)=Succ(Succ(Succ(Succ(x3)))) which results in the following new constraints: (12) (new_primModNatS02(x26, x25)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(Zero)))=x26 & Succ(Succ(Succ(Zero)))=x25 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) (13) (new_primModNatS01(x30, x29, x28, x27)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(Succ(x28))))=x30 & Succ(Succ(Succ(Succ(x27))))=x29 & (\/x31:new_primModNatS01(x30, x29, x28, x27)=Succ(Succ(Succ(Succ(x31)))) & Succ(Succ(Succ(x28)))=x30 & Succ(Succ(Succ(x27)))=x29 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x28)))))), Pos(Succ(Succ(Succ(Succ(Succ(x27)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x27)))))), Pos(new_primModNatS01(Succ(Succ(Succ(x28))), Succ(Succ(Succ(x27))), Succ(x28), Succ(x27))))) ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x27))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x27))))))), Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x28)))), Succ(Succ(Succ(Succ(x27)))), Succ(Succ(x28)), Succ(Succ(x27)))))) (14) (new_primModNatS02(x34, x33)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(Succ(x32))))=x34 & Succ(Succ(Succ(Zero)))=x33 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x32))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x32)))), Succ(Succ(Succ(Zero))), Succ(Succ(x32)), Succ(Zero))))) (15) (Succ(Succ(x37))=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(Zero)))=x37 & Succ(Succ(Succ(Succ(x35))))=x36 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))), Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x35)))), Succ(Zero), Succ(Succ(x35)))))) We simplified constraint (12) using rules (III), (IV) which results in the following new constraint: (16) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) We simplified constraint (13) using rules (III), (IV) which results in the following new constraint: (17) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x27))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x27))))))), Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x28)))), Succ(Succ(Succ(Succ(x27)))), Succ(Succ(x28)), Succ(Succ(x27)))))) We simplified constraint (14) using rules (III), (IV) which results in the following new constraint: (18) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x32))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x32)))), Succ(Succ(Succ(Zero))), Succ(Succ(x32)), Succ(Zero))))) We simplified constraint (15) using rules (I), (II), (III), (IV) which results in the following new constraint: (19) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))), Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x35)))), Succ(Zero), Succ(Succ(x35)))))) We simplified constraint (9) using rules (III), (IV), (VII) which results in the following new constraint: (20) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x13)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS01(Succ(Succ(Succ(x13))), Succ(Succ(Zero)), Succ(x13), Zero)))) To summarize, we get the following constraints P__>=_ for the following pairs. *new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))), Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x35)))), Succ(Zero), Succ(Succ(x35)))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x16)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x16)))))), Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x16))), Zero, Succ(x16))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x27))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x27))))))), Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x28)))), Succ(Succ(Succ(Succ(x27)))), Succ(Succ(x28)), Succ(Succ(x27)))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x32))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x32)))), Succ(Succ(Succ(Zero))), Succ(Succ(x32)), Succ(Zero))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x13)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS01(Succ(Succ(Succ(x13))), Succ(Succ(Zero)), Succ(x13), Zero)))) The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. ---------------------------------------- (120) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (121) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primRemInt(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Zero, vuz37300) -> Zero new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primRemInt(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primRemInt(Pos(x0), x1) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primRemInt(Neg(x0), x1) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primRemInt0(Pos(x0), x1) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (122) UsableRulesProof (EQUIVALENT) As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (123) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primRemInt(Pos(x0), x1) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primRemInt(Neg(x0), x1) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primRemInt0(Pos(x0), x1) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (124) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. new_primRemInt(Pos(x0), x1) new_primRemInt(Neg(x0), x1) ---------------------------------------- (125) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primRemInt0(Pos(x0), x1) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (126) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) at position [1] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1))),new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1)))) (new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1))),new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1)))) ---------------------------------------- (127) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primRemInt0(Pos(x0), x1) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (128) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. ---------------------------------------- (129) Complex Obligation (AND) ---------------------------------------- (130) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primRemInt0(Pos(x0), x1) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (131) UsableRulesProof (EQUIVALENT) As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (132) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primRemInt0(Pos(x0), x1) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (133) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. new_primRemInt0(Neg(x0), x1) new_primRemInt0(Pos(x0), x1) ---------------------------------------- (134) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (135) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero)))) (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1)))) (new_gcd0Gcd'(Neg(Zero), Neg(Succ(x0))) -> new_gcd0Gcd'(Neg(Succ(x0)), Neg(Zero)),new_gcd0Gcd'(Neg(Zero), Neg(Succ(x0))) -> new_gcd0Gcd'(Neg(Succ(x0)), Neg(Zero))) ---------------------------------------- (136) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Neg(Zero), Neg(Succ(x0))) -> new_gcd0Gcd'(Neg(Succ(x0)), Neg(Zero)) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (137) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node. ---------------------------------------- (138) Complex Obligation (AND) ---------------------------------------- (139) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (140) UsableRulesProof (EQUIVALENT) As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (141) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (142) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. new_primModNatS02(x0, x1) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) ---------------------------------------- (143) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (144) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (145) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (146) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (147) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (148) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (149) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (150) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) ---------------------------------------- (151) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (152) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (153) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (154) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (155) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (156) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (157) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (158) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) ---------------------------------------- (159) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (160) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (161) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (162) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (163) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (164) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (165) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (166) QDPSizeChangeProof (EQUIVALENT) We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. Order:Polynomial interpretation [POLO]: POL(Neg(x_1)) = x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 1 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 From the DPs we obtained the following set of size-change graphs: *new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 2 >= 1, 1 >= 2 *new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 2 >= 1, 1 > 2 We oriented the following set of usable rules [AAECC05,FROCOS05]. new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (167) YES ---------------------------------------- (168) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (169) UsableRulesProof (EQUIVALENT) As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (170) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (171) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS02(Zero, Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS02(Zero, Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS02(Succ(x2), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS02(Succ(x2), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))) ---------------------------------------- (172) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS02(Zero, Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS02(Succ(x2), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (173) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. ---------------------------------------- (174) Complex Obligation (AND) ---------------------------------------- (175) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS02(Zero, Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS02(Succ(x2), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (176) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS02(Zero, Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero))))) ---------------------------------------- (177) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS02(Succ(x2), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (178) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS02(Succ(x2), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero))))) ---------------------------------------- (179) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (180) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero))))) ---------------------------------------- (181) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (182) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero))))) ---------------------------------------- (183) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (184) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(Zero, Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(Zero, Succ(Zero))))) ---------------------------------------- (185) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(Zero, Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (186) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (187) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (188) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(Succ(x2), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(Succ(x2), Succ(Zero))))) ---------------------------------------- (189) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(Succ(x2), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (190) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(Succ(x2), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS01(x0, Zero, x0, Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS01(x0, Zero, x0, Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero)))) ---------------------------------------- (191) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS01(x0, Zero, x0, Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (192) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (193) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS01(x0, Zero, x0, Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (194) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS01(x0, Zero, x0, Zero))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Neg(x_1)) = 2*x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_gcd0Gcd'(x_1, x_2)) = 2*x_1 + 2*x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS01(x_1, x_2, x_3, x_4)) = 3 + x_1 POL(new_primModNatS02(x_1, x_2)) = 3 + x_1 POL(new_primModNatS1(x_1, x_2)) = 2 + x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (195) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (196) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (197) TRUE ---------------------------------------- (198) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (199) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Zero), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Zero), Succ(Zero))))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero))))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))) ---------------------------------------- (200) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Zero), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (201) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. ---------------------------------------- (202) Complex Obligation (AND) ---------------------------------------- (203) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Zero), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (204) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Zero), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero)))))) ---------------------------------------- (205) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (206) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero)))))) ---------------------------------------- (207) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (208) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero)))))) ---------------------------------------- (209) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (210) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero)))))) ---------------------------------------- (211) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (212) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero)))))) ---------------------------------------- (213) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (214) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero)))))) ---------------------------------------- (215) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (216) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Zero, Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Zero, Succ(Succ(Zero)))))) ---------------------------------------- (217) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Zero, Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (218) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (219) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (220) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero)))))) ---------------------------------------- (221) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (222) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Neg(x_1)) = 2*x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_gcd0Gcd'(x_1, x_2)) = 2*x_1 + 2*x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS01(x_1, x_2, x_3, x_4)) = 2 + x_1 POL(new_primModNatS02(x_1, x_2)) = 1 + x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (223) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (224) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (225) TRUE ---------------------------------------- (226) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (227) InductionCalculusProof (EQUIVALENT) Note that final constraints are written in bold face. For Pair new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) the following chains were created: *We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Succ(Succ(x1)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x1))))), Neg(new_primModNatS01(Succ(Succ(x0)), Succ(Succ(x1)), x0, x1))), new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) which results in the following constraint: (1) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x1))))), Neg(new_primModNatS01(Succ(Succ(x0)), Succ(Succ(x1)), x0, x1)))=new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Succ(Succ(x1))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x1))))), Neg(new_primModNatS01(Succ(Succ(x0)), Succ(Succ(x1)), x0, x1)))) We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint: (2) (Succ(Succ(x0))=x4 & Succ(Succ(x1))=x5 & new_primModNatS01(x4, x5, x0, x1)=Succ(Succ(Succ(Succ(x3)))) ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Succ(Succ(x1))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x1))))), Neg(new_primModNatS01(Succ(Succ(x0)), Succ(Succ(x1)), x0, x1)))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x4, x5, x0, x1)=Succ(Succ(Succ(Succ(x3)))) which results in the following new constraints: (3) (new_primModNatS02(x7, x6)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Zero))=x7 & Succ(Succ(Zero))=x6 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) (4) (new_primModNatS01(x11, x10, x9, x8)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(x9)))=x11 & Succ(Succ(Succ(x8)))=x10 & (\/x12:new_primModNatS01(x11, x10, x9, x8)=Succ(Succ(Succ(Succ(x12)))) & Succ(Succ(x9))=x11 & Succ(Succ(x8))=x10 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x9))))), Neg(Succ(Succ(Succ(Succ(x8))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x8))))), Neg(new_primModNatS01(Succ(Succ(x9)), Succ(Succ(x8)), x9, x8)))) ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x9)))))), Neg(Succ(Succ(Succ(Succ(Succ(x8)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x8)))))), Neg(new_primModNatS01(Succ(Succ(Succ(x9))), Succ(Succ(Succ(x8))), Succ(x9), Succ(x8))))) (5) (new_primModNatS02(x15, x14)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(x13)))=x15 & Succ(Succ(Zero))=x14 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x13)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS01(Succ(Succ(Succ(x13))), Succ(Succ(Zero)), Succ(x13), Zero)))) (6) (Succ(Succ(x18))=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Zero))=x18 & Succ(Succ(Succ(x16)))=x17 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x16)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x16)))))), Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x16))), Zero, Succ(x16))))) We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x7, x6)=Succ(Succ(Succ(Succ(x3)))) which results in the following new constraint: (7) (new_primModNatS1(new_primMinusNatS0(Succ(x20), Succ(x19)), Succ(x19))=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Zero))=x20 & Succ(Succ(Zero))=x19 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) We simplified constraint (4) using rule (IV) which results in the following new constraint: (8) (new_primModNatS01(x11, x10, x9, x8)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(x9)))=x11 & Succ(Succ(Succ(x8)))=x10 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x9)))))), Neg(Succ(Succ(Succ(Succ(Succ(x8)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x8)))))), Neg(new_primModNatS01(Succ(Succ(Succ(x9))), Succ(Succ(Succ(x8))), Succ(x9), Succ(x8))))) We simplified constraint (5) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x15, x14)=Succ(Succ(Succ(Succ(x3)))) which results in the following new constraint: (9) (new_primModNatS1(new_primMinusNatS0(Succ(x39), Succ(x38)), Succ(x38))=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(x13)))=x39 & Succ(Succ(Zero))=x38 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x13)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS01(Succ(Succ(Succ(x13))), Succ(Succ(Zero)), Succ(x13), Zero)))) We simplified constraint (6) using rules (I), (II), (III), (IV) which results in the following new constraint: (10) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x16)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x16)))))), Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x16))), Zero, Succ(x16))))) We simplified constraint (7) using rules (III), (IV), (VII) which results in the following new constraint: (11) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x11, x10, x9, x8)=Succ(Succ(Succ(Succ(x3)))) which results in the following new constraints: (12) (new_primModNatS02(x26, x25)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(Zero)))=x26 & Succ(Succ(Succ(Zero)))=x25 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) (13) (new_primModNatS01(x30, x29, x28, x27)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(Succ(x28))))=x30 & Succ(Succ(Succ(Succ(x27))))=x29 & (\/x31:new_primModNatS01(x30, x29, x28, x27)=Succ(Succ(Succ(Succ(x31)))) & Succ(Succ(Succ(x28)))=x30 & Succ(Succ(Succ(x27)))=x29 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x28)))))), Neg(Succ(Succ(Succ(Succ(Succ(x27)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x27)))))), Neg(new_primModNatS01(Succ(Succ(Succ(x28))), Succ(Succ(Succ(x27))), Succ(x28), Succ(x27))))) ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x27))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x27))))))), Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x28)))), Succ(Succ(Succ(Succ(x27)))), Succ(Succ(x28)), Succ(Succ(x27)))))) (14) (new_primModNatS02(x34, x33)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(Succ(x32))))=x34 & Succ(Succ(Succ(Zero)))=x33 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x32))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x32)))), Succ(Succ(Succ(Zero))), Succ(Succ(x32)), Succ(Zero))))) (15) (Succ(Succ(x37))=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(Zero)))=x37 & Succ(Succ(Succ(Succ(x35))))=x36 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))), Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x35)))), Succ(Zero), Succ(Succ(x35)))))) We simplified constraint (12) using rules (III), (IV) which results in the following new constraint: (16) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) We simplified constraint (13) using rules (III), (IV) which results in the following new constraint: (17) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x27))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x27))))))), Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x28)))), Succ(Succ(Succ(Succ(x27)))), Succ(Succ(x28)), Succ(Succ(x27)))))) We simplified constraint (14) using rules (III), (IV) which results in the following new constraint: (18) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x32))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x32)))), Succ(Succ(Succ(Zero))), Succ(Succ(x32)), Succ(Zero))))) We simplified constraint (15) using rules (I), (II), (III), (IV) which results in the following new constraint: (19) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))), Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x35)))), Succ(Zero), Succ(Succ(x35)))))) We simplified constraint (9) using rules (III), (IV), (VII) which results in the following new constraint: (20) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x13)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS01(Succ(Succ(Succ(x13))), Succ(Succ(Zero)), Succ(x13), Zero)))) To summarize, we get the following constraints P__>=_ for the following pairs. *new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))), Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x35)))), Succ(Zero), Succ(Succ(x35)))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x16)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x16)))))), Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x16))), Zero, Succ(x16))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x27))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x27))))))), Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x28)))), Succ(Succ(Succ(Succ(x27)))), Succ(Succ(x28)), Succ(Succ(x27)))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x32))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x32)))), Succ(Succ(Succ(Zero))), Succ(Succ(x32)), Succ(Zero))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x13)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS01(Succ(Succ(Succ(x13))), Succ(Succ(Zero)), Succ(x13), Zero)))) The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. ---------------------------------------- (228) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (229) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primRemInt0(Pos(x0), x1) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (230) UsableRulesProof (EQUIVALENT) As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (231) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primRemInt0(Pos(x0), x1) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (232) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. new_primRemInt0(Neg(x0), x1) new_primRemInt0(Pos(x0), x1) ---------------------------------------- (233) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (234) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero)))) (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS01(x0, x1, x0, x1))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS01(x0, x1, x0, x1)))) (new_gcd0Gcd'(Pos(Zero), Neg(Succ(x0))) -> new_gcd0Gcd'(Neg(Succ(x0)), Pos(Zero)),new_gcd0Gcd'(Pos(Zero), Neg(Succ(x0))) -> new_gcd0Gcd'(Neg(Succ(x0)), Pos(Zero))) ---------------------------------------- (235) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Zero), Neg(Succ(x0))) -> new_gcd0Gcd'(Neg(Succ(x0)), Pos(Zero)) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (236) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (237) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS01(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (238) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (239) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (240) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (241) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS01(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (242) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (243) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (244) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero)))) (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1)))) (new_gcd0Gcd'(Neg(Zero), Pos(Succ(x0))) -> new_gcd0Gcd'(Pos(Succ(x0)), Neg(Zero)),new_gcd0Gcd'(Neg(Zero), Pos(Succ(x0))) -> new_gcd0Gcd'(Pos(Succ(x0)), Neg(Zero))) ---------------------------------------- (245) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Neg(Zero), Pos(Succ(x0))) -> new_gcd0Gcd'(Pos(Succ(x0)), Neg(Zero)) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (246) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs with 2 less nodes. ---------------------------------------- (247) Complex Obligation (AND) ---------------------------------------- (248) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (249) UsableRulesProof (EQUIVALENT) As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (250) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (251) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. new_primModNatS02(x0, x1) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) ---------------------------------------- (252) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (253) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (254) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (255) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) ---------------------------------------- (256) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (257) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (258) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (259) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (260) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (261) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (262) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (263) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) ---------------------------------------- (264) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (265) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (266) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (267) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (268) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (269) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (270) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (271) QDPSizeChangeProof (EQUIVALENT) We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. Order:Polynomial interpretation [POLO]: POL(Neg(x_1)) = x_1 POL(Pos(x_1)) = 1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 1 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 From the DPs we obtained the following set of size-change graphs: *new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 2 >= 1, 1 >= 2 *new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 2 >= 1, 1 > 2 We oriented the following set of usable rules [AAECC05,FROCOS05]. new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (272) YES ---------------------------------------- (273) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (274) UsableRulesProof (EQUIVALENT) As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (275) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (276) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. new_primModNatS02(x0, x1) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) ---------------------------------------- (277) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (278) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) ---------------------------------------- (279) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (280) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (281) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (282) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (283) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (284) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (285) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (286) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) ---------------------------------------- (287) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (288) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (289) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (290) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (291) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (292) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (293) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (294) QDPSizeChangeProof (EQUIVALENT) We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. Order:Polynomial interpretation [POLO]: POL(Neg(x_1)) = 1 POL(Pos(x_1)) = x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 1 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 From the DPs we obtained the following set of size-change graphs: *new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 2 >= 1, 1 >= 2 *new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 2 >= 1, 1 > 2 We oriented the following set of usable rules [AAECC05,FROCOS05]. new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (295) YES ---------------------------------------- (296) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (297) UsableRulesProof (EQUIVALENT) As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (298) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (299) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS01(x0, x1, x0, x1))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS02(Zero, Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS02(Zero, Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS02(Succ(x2), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS02(Succ(x2), Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))) ---------------------------------------- (300) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS02(Zero, Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS02(Succ(x2), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (301) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS02(Zero, Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero))))) ---------------------------------------- (302) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS02(Succ(x2), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (303) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS02(Succ(x2), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero))))) ---------------------------------------- (304) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (305) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero))))) ---------------------------------------- (306) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (307) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero))))) ---------------------------------------- (308) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (309) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Zero, Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Zero, Succ(Zero))))) ---------------------------------------- (310) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Zero, Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (311) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (312) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (313) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero))))) ---------------------------------------- (314) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (315) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Zero), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Zero), Succ(Zero))))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero))))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))) ---------------------------------------- (316) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Zero), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (317) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Zero), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero)))))) ---------------------------------------- (318) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (319) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero)))))) ---------------------------------------- (320) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (321) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero)))))) ---------------------------------------- (322) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (323) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero)))))) ---------------------------------------- (324) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (325) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero)))))) ---------------------------------------- (326) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (327) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero)))))) ---------------------------------------- (328) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (329) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Zero, Succ(Succ(Zero)))))) ---------------------------------------- (330) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (331) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (332) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (333) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero)))))) ---------------------------------------- (334) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (335) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS01(x0, x1, x0, x1))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS02(Zero, Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS02(Zero, Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS02(Succ(x2), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS02(Succ(x2), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))) ---------------------------------------- (336) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS02(Zero, Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS02(Succ(x2), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (337) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs with 1 less node. ---------------------------------------- (338) Complex Obligation (AND) ---------------------------------------- (339) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS02(Succ(x2), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (340) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS02(Succ(x2), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero))))) ---------------------------------------- (341) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (342) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero))))) ---------------------------------------- (343) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (344) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(Succ(x2), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(Succ(x2), Succ(Zero))))) ---------------------------------------- (345) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(Succ(x2), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (346) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(Succ(x2), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS01(x0, Zero, x0, Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS01(x0, Zero, x0, Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero)))) ---------------------------------------- (347) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS01(x0, Zero, x0, Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (348) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (349) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS01(x0, Zero, x0, Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (350) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS01(x0, Zero, x0, Zero))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Neg(x_1)) = x_1 POL(Pos(x_1)) = 0 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_gcd0Gcd'(x_1, x_2)) = 2*x_1 + 2*x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS01(x_1, x_2, x_3, x_4)) = 2 + x_1 POL(new_primModNatS02(x_1, x_2)) = 2 + x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (351) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (352) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (353) TRUE ---------------------------------------- (354) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (355) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS01(x0, Zero, x0, Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS01(x0, Zero, x0, Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero)))) ---------------------------------------- (356) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS01(x0, Zero, x0, Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (357) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (358) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS01(x0, Zero, x0, Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (359) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS01(x0, Zero, x0, Zero))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Neg(x_1)) = 0 POL(Pos(x_1)) = x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_gcd0Gcd'(x_1, x_2)) = 2*x_1 + 2*x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS01(x_1, x_2, x_3, x_4)) = 2 + x_1 POL(new_primModNatS02(x_1, x_2)) = 2 + x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (360) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (361) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (362) TRUE ---------------------------------------- (363) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (364) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Zero), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Zero), Succ(Zero))))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero))))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))) ---------------------------------------- (365) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Zero), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (366) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs with 1 less node. ---------------------------------------- (367) Complex Obligation (AND) ---------------------------------------- (368) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (369) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero)))))) ---------------------------------------- (370) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (371) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero)))))) ---------------------------------------- (372) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (373) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero)))))) ---------------------------------------- (374) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (375) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero)))))) ---------------------------------------- (376) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (377) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Neg(x_1)) = 2*x_1 POL(Pos(x_1)) = 0 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_gcd0Gcd'(x_1, x_2)) = 2*x_1 + 2*x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS01(x_1, x_2, x_3, x_4)) = 2 + x_1 POL(new_primModNatS02(x_1, x_2)) = 1 + x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (378) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (379) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (380) TRUE ---------------------------------------- (381) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (382) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Neg(x_1)) = 0 POL(Pos(x_1)) = 2*x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_gcd0Gcd'(x_1, x_2)) = 2*x_1 + 2*x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS01(x_1, x_2, x_3, x_4)) = 2 + x_1 POL(new_primModNatS02(x_1, x_2)) = 1 + x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (383) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (384) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (385) TRUE ---------------------------------------- (386) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (387) InductionCalculusProof (EQUIVALENT) Note that final constraints are written in bold face. For Pair new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) the following chains were created: *We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x4))))), Neg(Succ(Succ(Succ(Succ(x5)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x5))))), Pos(new_primModNatS01(Succ(Succ(x4)), Succ(Succ(x5)), x4, x5))) which results in the following constraint: (1) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3)))=new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x4))))), Neg(Succ(Succ(Succ(Succ(x5)))))) ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3)))) We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint: (2) (Succ(Succ(x2))=x12 & Succ(Succ(x3))=x13 & new_primModNatS01(x12, x13, x2, x3)=Succ(Succ(Succ(Succ(x5)))) ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3)))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x12, x13, x2, x3)=Succ(Succ(Succ(Succ(x5)))) which results in the following new constraints: (3) (new_primModNatS02(x15, x14)=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Zero))=x15 & Succ(Succ(Zero))=x14 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) (4) (new_primModNatS01(x19, x18, x17, x16)=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Succ(x17)))=x19 & Succ(Succ(Succ(x16)))=x18 & (\/x20:new_primModNatS01(x19, x18, x17, x16)=Succ(Succ(Succ(Succ(x20)))) & Succ(Succ(x17))=x19 & Succ(Succ(x16))=x18 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x17))))), Pos(Succ(Succ(Succ(Succ(x16))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x16))))), Neg(new_primModNatS01(Succ(Succ(x17)), Succ(Succ(x16)), x17, x16)))) ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x17)))))), Pos(Succ(Succ(Succ(Succ(Succ(x16)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x16)))))), Neg(new_primModNatS01(Succ(Succ(Succ(x17))), Succ(Succ(Succ(x16))), Succ(x17), Succ(x16))))) (5) (new_primModNatS02(x23, x22)=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Succ(x21)))=x23 & Succ(Succ(Zero))=x22 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x21)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS01(Succ(Succ(Succ(x21))), Succ(Succ(Zero)), Succ(x21), Zero)))) (6) (Succ(Succ(x26))=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Zero))=x26 & Succ(Succ(Succ(x24)))=x25 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x24)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x24)))))), Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x24))), Zero, Succ(x24))))) We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x15, x14)=Succ(Succ(Succ(Succ(x5)))) which results in the following new constraint: (7) (new_primModNatS1(new_primMinusNatS0(Succ(x28), Succ(x27)), Succ(x27))=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Zero))=x28 & Succ(Succ(Zero))=x27 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) We simplified constraint (4) using rule (IV) which results in the following new constraint: (8) (new_primModNatS01(x19, x18, x17, x16)=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Succ(x17)))=x19 & Succ(Succ(Succ(x16)))=x18 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x17)))))), Pos(Succ(Succ(Succ(Succ(Succ(x16)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x16)))))), Neg(new_primModNatS01(Succ(Succ(Succ(x17))), Succ(Succ(Succ(x16))), Succ(x17), Succ(x16))))) We simplified constraint (5) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x23, x22)=Succ(Succ(Succ(Succ(x5)))) which results in the following new constraint: (9) (new_primModNatS1(new_primMinusNatS0(Succ(x47), Succ(x46)), Succ(x46))=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Succ(x21)))=x47 & Succ(Succ(Zero))=x46 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x21)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS01(Succ(Succ(Succ(x21))), Succ(Succ(Zero)), Succ(x21), Zero)))) We simplified constraint (6) using rules (I), (II), (III), (IV) which results in the following new constraint: (10) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x24)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x24)))))), Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x24))), Zero, Succ(x24))))) We simplified constraint (7) using rules (III), (IV), (VII) which results in the following new constraint: (11) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x19, x18, x17, x16)=Succ(Succ(Succ(Succ(x5)))) which results in the following new constraints: (12) (new_primModNatS02(x34, x33)=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Succ(Zero)))=x34 & Succ(Succ(Succ(Zero)))=x33 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) (13) (new_primModNatS01(x38, x37, x36, x35)=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Succ(Succ(x36))))=x38 & Succ(Succ(Succ(Succ(x35))))=x37 & (\/x39:new_primModNatS01(x38, x37, x36, x35)=Succ(Succ(Succ(Succ(x39)))) & Succ(Succ(Succ(x36)))=x38 & Succ(Succ(Succ(x35)))=x37 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x36)))))), Pos(Succ(Succ(Succ(Succ(Succ(x35)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x35)))))), Neg(new_primModNatS01(Succ(Succ(Succ(x36))), Succ(Succ(Succ(x35))), Succ(x36), Succ(x35))))) ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x36))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))), Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x36)))), Succ(Succ(Succ(Succ(x35)))), Succ(Succ(x36)), Succ(Succ(x35)))))) (14) (new_primModNatS02(x42, x41)=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Succ(Succ(x40))))=x42 & Succ(Succ(Succ(Zero)))=x41 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x40))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x40)))), Succ(Succ(Succ(Zero))), Succ(Succ(x40)), Succ(Zero))))) (15) (Succ(Succ(x45))=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Succ(Zero)))=x45 & Succ(Succ(Succ(Succ(x43))))=x44 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x43))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x43))))))), Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x43)))), Succ(Zero), Succ(Succ(x43)))))) We simplified constraint (12) using rules (III), (IV) which results in the following new constraint: (16) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) We simplified constraint (13) using rules (III), (IV) which results in the following new constraint: (17) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x36))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))), Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x36)))), Succ(Succ(Succ(Succ(x35)))), Succ(Succ(x36)), Succ(Succ(x35)))))) We simplified constraint (14) using rules (III), (IV) which results in the following new constraint: (18) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x40))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x40)))), Succ(Succ(Succ(Zero))), Succ(Succ(x40)), Succ(Zero))))) We simplified constraint (15) using rules (I), (II), (III), (IV) which results in the following new constraint: (19) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x43))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x43))))))), Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x43)))), Succ(Zero), Succ(Succ(x43)))))) We simplified constraint (9) using rules (III), (IV), (VII) which results in the following new constraint: (20) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x21)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS01(Succ(Succ(Succ(x21))), Succ(Succ(Zero)), Succ(x21), Zero)))) For Pair new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) the following chains were created: *We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x6))))), Neg(Succ(Succ(Succ(Succ(x7)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x7))))), Pos(new_primModNatS01(Succ(Succ(x6)), Succ(Succ(x7)), x6, x7))), new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x8))))), Pos(Succ(Succ(Succ(Succ(x9)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x9))))), Neg(new_primModNatS01(Succ(Succ(x8)), Succ(Succ(x9)), x8, x9))) which results in the following constraint: (1) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x7))))), Pos(new_primModNatS01(Succ(Succ(x6)), Succ(Succ(x7)), x6, x7)))=new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x8))))), Pos(Succ(Succ(Succ(Succ(x9)))))) ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x6))))), Neg(Succ(Succ(Succ(Succ(x7))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x7))))), Pos(new_primModNatS01(Succ(Succ(x6)), Succ(Succ(x7)), x6, x7)))) We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint: (2) (Succ(Succ(x6))=x52 & Succ(Succ(x7))=x53 & new_primModNatS01(x52, x53, x6, x7)=Succ(Succ(Succ(Succ(x9)))) ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x6))))), Neg(Succ(Succ(Succ(Succ(x7))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x7))))), Pos(new_primModNatS01(Succ(Succ(x6)), Succ(Succ(x7)), x6, x7)))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x52, x53, x6, x7)=Succ(Succ(Succ(Succ(x9)))) which results in the following new constraints: (3) (new_primModNatS02(x55, x54)=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Zero))=x55 & Succ(Succ(Zero))=x54 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) (4) (new_primModNatS01(x59, x58, x57, x56)=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Succ(x57)))=x59 & Succ(Succ(Succ(x56)))=x58 & (\/x60:new_primModNatS01(x59, x58, x57, x56)=Succ(Succ(Succ(Succ(x60)))) & Succ(Succ(x57))=x59 & Succ(Succ(x56))=x58 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x57))))), Neg(Succ(Succ(Succ(Succ(x56))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x56))))), Pos(new_primModNatS01(Succ(Succ(x57)), Succ(Succ(x56)), x57, x56)))) ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x57)))))), Neg(Succ(Succ(Succ(Succ(Succ(x56)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x56)))))), Pos(new_primModNatS01(Succ(Succ(Succ(x57))), Succ(Succ(Succ(x56))), Succ(x57), Succ(x56))))) (5) (new_primModNatS02(x63, x62)=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Succ(x61)))=x63 & Succ(Succ(Zero))=x62 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x61)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS01(Succ(Succ(Succ(x61))), Succ(Succ(Zero)), Succ(x61), Zero)))) (6) (Succ(Succ(x66))=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Zero))=x66 & Succ(Succ(Succ(x64)))=x65 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x64)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x64)))))), Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x64))), Zero, Succ(x64))))) We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x55, x54)=Succ(Succ(Succ(Succ(x9)))) which results in the following new constraint: (7) (new_primModNatS1(new_primMinusNatS0(Succ(x68), Succ(x67)), Succ(x67))=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Zero))=x68 & Succ(Succ(Zero))=x67 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) We simplified constraint (4) using rule (IV) which results in the following new constraint: (8) (new_primModNatS01(x59, x58, x57, x56)=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Succ(x57)))=x59 & Succ(Succ(Succ(x56)))=x58 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x57)))))), Neg(Succ(Succ(Succ(Succ(Succ(x56)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x56)))))), Pos(new_primModNatS01(Succ(Succ(Succ(x57))), Succ(Succ(Succ(x56))), Succ(x57), Succ(x56))))) We simplified constraint (5) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x63, x62)=Succ(Succ(Succ(Succ(x9)))) which results in the following new constraint: (9) (new_primModNatS1(new_primMinusNatS0(Succ(x87), Succ(x86)), Succ(x86))=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Succ(x61)))=x87 & Succ(Succ(Zero))=x86 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x61)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS01(Succ(Succ(Succ(x61))), Succ(Succ(Zero)), Succ(x61), Zero)))) We simplified constraint (6) using rules (I), (II), (III), (IV) which results in the following new constraint: (10) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x64)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x64)))))), Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x64))), Zero, Succ(x64))))) We simplified constraint (7) using rules (III), (IV), (VII) which results in the following new constraint: (11) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x59, x58, x57, x56)=Succ(Succ(Succ(Succ(x9)))) which results in the following new constraints: (12) (new_primModNatS02(x74, x73)=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Succ(Zero)))=x74 & Succ(Succ(Succ(Zero)))=x73 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) (13) (new_primModNatS01(x78, x77, x76, x75)=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Succ(Succ(x76))))=x78 & Succ(Succ(Succ(Succ(x75))))=x77 & (\/x79:new_primModNatS01(x78, x77, x76, x75)=Succ(Succ(Succ(Succ(x79)))) & Succ(Succ(Succ(x76)))=x78 & Succ(Succ(Succ(x75)))=x77 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x76)))))), Neg(Succ(Succ(Succ(Succ(Succ(x75)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x75)))))), Pos(new_primModNatS01(Succ(Succ(Succ(x76))), Succ(Succ(Succ(x75))), Succ(x76), Succ(x75))))) ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x76))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x75))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x75))))))), Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x76)))), Succ(Succ(Succ(Succ(x75)))), Succ(Succ(x76)), Succ(Succ(x75)))))) (14) (new_primModNatS02(x82, x81)=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Succ(Succ(x80))))=x82 & Succ(Succ(Succ(Zero)))=x81 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x80))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x80)))), Succ(Succ(Succ(Zero))), Succ(Succ(x80)), Succ(Zero))))) (15) (Succ(Succ(x85))=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Succ(Zero)))=x85 & Succ(Succ(Succ(Succ(x83))))=x84 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x83))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x83))))))), Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x83)))), Succ(Zero), Succ(Succ(x83)))))) We simplified constraint (12) using rules (III), (IV) which results in the following new constraint: (16) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) We simplified constraint (13) using rules (III), (IV) which results in the following new constraint: (17) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x76))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x75))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x75))))))), Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x76)))), Succ(Succ(Succ(Succ(x75)))), Succ(Succ(x76)), Succ(Succ(x75)))))) We simplified constraint (14) using rules (III), (IV) which results in the following new constraint: (18) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x80))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x80)))), Succ(Succ(Succ(Zero))), Succ(Succ(x80)), Succ(Zero))))) We simplified constraint (15) using rules (I), (II), (III), (IV) which results in the following new constraint: (19) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x83))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x83))))))), Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x83)))), Succ(Zero), Succ(Succ(x83)))))) We simplified constraint (9) using rules (III), (IV), (VII) which results in the following new constraint: (20) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x61)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS01(Succ(Succ(Succ(x61))), Succ(Succ(Zero)), Succ(x61), Zero)))) To summarize, we get the following constraints P__>=_ for the following pairs. *new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x43))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x43))))))), Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x43)))), Succ(Zero), Succ(Succ(x43)))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x24)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x24)))))), Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x24))), Zero, Succ(x24))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x36))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))), Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x36)))), Succ(Succ(Succ(Succ(x35)))), Succ(Succ(x36)), Succ(Succ(x35)))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x40))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x40)))), Succ(Succ(Succ(Zero))), Succ(Succ(x40)), Succ(Zero))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x21)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS01(Succ(Succ(Succ(x21))), Succ(Succ(Zero)), Succ(x21), Zero)))) *new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x83))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x83))))))), Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x83)))), Succ(Zero), Succ(Succ(x83)))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x64)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x64)))))), Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x64))), Zero, Succ(x64))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x76))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x75))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x75))))))), Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x76)))), Succ(Succ(Succ(Succ(x75)))), Succ(Succ(x76)), Succ(Succ(x75)))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x80))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x80)))), Succ(Succ(Succ(Zero))), Succ(Succ(x80)), Succ(Zero))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x61)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS01(Succ(Succ(Succ(x61))), Succ(Succ(Zero)), Succ(x61), Zero)))) The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. ---------------------------------------- (388) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS01(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS01(vuz391, vuz392, Zero, Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS02(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS01(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS01(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS02(vuz391, vuz392) new_primModNatS01(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (389) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMulNat(Succ(vuz310000), vuz4100) -> new_primMulNat(vuz310000, vuz4100) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (390) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_primMulNat(Succ(vuz310000), vuz4100) -> new_primMulNat(vuz310000, vuz4100) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (391) YES ---------------------------------------- (392) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd2(Succ(vuz2870), Succ(vuz3030), vuz68) -> new_gcd2(vuz2870, vuz3030, vuz68) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (393) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_gcd2(Succ(vuz2870), Succ(vuz3030), vuz68) -> new_gcd2(vuz2870, vuz3030, vuz68) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 ---------------------------------------- (394) YES ---------------------------------------- (395) Obligation: Q DP problem: The TRS P consists of the following rules: new_primQuotInt(Succ(vuz1690), Succ(vuz2050), vuz68) -> new_primQuotInt(vuz1690, vuz2050, vuz68) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (396) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_primQuotInt(Succ(vuz1690), Succ(vuz2050), vuz68) -> new_primQuotInt(vuz1690, vuz2050, vuz68) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 ---------------------------------------- (397) YES ---------------------------------------- (398) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS(Succ(Zero), Zero) -> new_primModNatS(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS0(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS00(vuz391, vuz392) -> new_primModNatS(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS(Succ(Succ(vuz374000)), Zero) -> new_primModNatS(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS0(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS0(vuz391, vuz392, Zero, Zero) -> new_primModNatS00(vuz391, vuz392) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (399) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node. ---------------------------------------- (400) Complex Obligation (AND) ---------------------------------------- (401) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS0(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS0(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS0(vuz391, vuz392, Zero, Zero) -> new_primModNatS00(vuz391, vuz392) new_primModNatS00(vuz391, vuz392) -> new_primModNatS(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (402) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) at position [0] we obtained the following new rules [LPAR04]: (new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392)),new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392))) ---------------------------------------- (403) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS0(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS0(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS0(vuz391, vuz392, Zero, Zero) -> new_primModNatS00(vuz391, vuz392) new_primModNatS00(vuz391, vuz392) -> new_primModNatS(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392)) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (404) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_primModNatS00(vuz391, vuz392) -> new_primModNatS(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) at position [0] we obtained the following new rules [LPAR04]: (new_primModNatS00(vuz391, vuz392) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392)),new_primModNatS00(vuz391, vuz392) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392))) ---------------------------------------- (405) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS0(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS0(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS0(vuz391, vuz392, Zero, Zero) -> new_primModNatS00(vuz391, vuz392) new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392)) new_primModNatS00(vuz391, vuz392) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392)) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (406) QDPSizeChangeProof (EQUIVALENT) We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. Order:Polynomial interpretation [POLO]: POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 1 POL(new_primMinusNatS0(x_1, x_2)) = x_1 From the DPs we obtained the following set of size-change graphs: *new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392)) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 1 >= 1 *new_primModNatS00(vuz391, vuz392) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392)) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 1 >= 1 *new_primModNatS(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS0(vuz374000, vuz373000, vuz374000, vuz373000) (allowed arguments on rhs = {1, 2, 3, 4}) The graph contains the following edges 1 > 1, 2 > 2, 1 > 3, 2 > 4 *new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS0(vuz391, vuz392, vuz3930, vuz3940) (allowed arguments on rhs = {1, 2, 3, 4}) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 *new_primModNatS0(vuz391, vuz392, Zero, Zero) -> new_primModNatS00(vuz391, vuz392) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 1 >= 1, 2 >= 2 We oriented the following set of usable rules [AAECC05,FROCOS05]. new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) ---------------------------------------- (407) YES ---------------------------------------- (408) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS(Succ(Succ(vuz374000)), Zero) -> new_primModNatS(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (409) QDPSizeChangeProof (EQUIVALENT) We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. Order:Polynomial interpretation [POLO]: POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 1 POL(new_primMinusNatS0(x_1, x_2)) = x_1 From the DPs we obtained the following set of size-change graphs: *new_primModNatS(Succ(Succ(vuz374000)), Zero) -> new_primModNatS(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 1 > 1, 2 >= 2 We oriented the following set of usable rules [AAECC05,FROCOS05]. new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (410) YES ---------------------------------------- (411) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS(Succ(Succ(vuz28000)), Succ(vuz281000)) -> new_primDivNatS0(vuz28000, vuz281000, vuz28000, vuz281000) new_primDivNatS0(vuz338, vuz339, Succ(vuz3400), Zero) -> new_primDivNatS(new_primMinusNatS0(vuz338, vuz339), Succ(vuz339)) new_primDivNatS0(vuz338, vuz339, Zero, Zero) -> new_primDivNatS00(vuz338, vuz339) new_primDivNatS0(vuz338, vuz339, Succ(vuz3400), Succ(vuz3410)) -> new_primDivNatS0(vuz338, vuz339, vuz3400, vuz3410) new_primDivNatS(Succ(Zero), Zero) -> new_primDivNatS(new_primMinusNatS2, Zero) new_primDivNatS(Succ(Succ(vuz28000)), Zero) -> new_primDivNatS(new_primMinusNatS1(vuz28000), Zero) new_primDivNatS00(vuz338, vuz339) -> new_primDivNatS(new_primMinusNatS0(vuz338, vuz339), Succ(vuz339)) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS1(vuz28000) -> Succ(vuz28000) new_primMinusNatS2 -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS2 new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primMinusNatS1(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (412) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node. ---------------------------------------- (413) Complex Obligation (AND) ---------------------------------------- (414) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS(Succ(Succ(vuz28000)), Zero) -> new_primDivNatS(new_primMinusNatS1(vuz28000), Zero) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS1(vuz28000) -> Succ(vuz28000) new_primMinusNatS2 -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS2 new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primMinusNatS1(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (415) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: new_primDivNatS(Succ(Succ(vuz28000)), Zero) -> new_primDivNatS(new_primMinusNatS1(vuz28000), Zero) Strictly oriented rules of the TRS R: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS1(vuz28000) -> Succ(vuz28000) new_primMinusNatS2 -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) Used ordering: Polynomial interpretation [POLO]: POL(Succ(x_1)) = 1 + 2*x_1 POL(Zero) = 1 POL(new_primDivNatS(x_1, x_2)) = x_1 + x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 + x_2 POL(new_primMinusNatS1(x_1)) = 2 + 2*x_1 POL(new_primMinusNatS2) = 2 ---------------------------------------- (416) Obligation: Q DP problem: P is empty. R is empty. The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS2 new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primMinusNatS1(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (417) PisEmptyProof (EQUIVALENT) The TRS P is empty. Hence, there is no (P,Q,R) chain. ---------------------------------------- (418) YES ---------------------------------------- (419) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS0(vuz338, vuz339, Succ(vuz3400), Zero) -> new_primDivNatS(new_primMinusNatS0(vuz338, vuz339), Succ(vuz339)) new_primDivNatS(Succ(Succ(vuz28000)), Succ(vuz281000)) -> new_primDivNatS0(vuz28000, vuz281000, vuz28000, vuz281000) new_primDivNatS0(vuz338, vuz339, Zero, Zero) -> new_primDivNatS00(vuz338, vuz339) new_primDivNatS00(vuz338, vuz339) -> new_primDivNatS(new_primMinusNatS0(vuz338, vuz339), Succ(vuz339)) new_primDivNatS0(vuz338, vuz339, Succ(vuz3400), Succ(vuz3410)) -> new_primDivNatS0(vuz338, vuz339, vuz3400, vuz3410) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS1(vuz28000) -> Succ(vuz28000) new_primMinusNatS2 -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS2 new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primMinusNatS1(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (420) QDPSizeChangeProof (EQUIVALENT) We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. Order:Polynomial interpretation [POLO]: POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 1 POL(new_primMinusNatS0(x_1, x_2)) = x_1 From the DPs we obtained the following set of size-change graphs: *new_primDivNatS(Succ(Succ(vuz28000)), Succ(vuz281000)) -> new_primDivNatS0(vuz28000, vuz281000, vuz28000, vuz281000) (allowed arguments on rhs = {1, 2, 3, 4}) The graph contains the following edges 1 > 1, 2 > 2, 1 > 3, 2 > 4 *new_primDivNatS0(vuz338, vuz339, Succ(vuz3400), Succ(vuz3410)) -> new_primDivNatS0(vuz338, vuz339, vuz3400, vuz3410) (allowed arguments on rhs = {1, 2, 3, 4}) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 *new_primDivNatS0(vuz338, vuz339, Succ(vuz3400), Zero) -> new_primDivNatS(new_primMinusNatS0(vuz338, vuz339), Succ(vuz339)) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 1 >= 1 *new_primDivNatS0(vuz338, vuz339, Zero, Zero) -> new_primDivNatS00(vuz338, vuz339) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 1 >= 1, 2 >= 2 *new_primDivNatS00(vuz338, vuz339) -> new_primDivNatS(new_primMinusNatS0(vuz338, vuz339), Succ(vuz339)) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 1 >= 1 We oriented the following set of usable rules [AAECC05,FROCOS05]. new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) ---------------------------------------- (421) YES ---------------------------------------- (422) Obligation: Q DP problem: The TRS P consists of the following rules: new_primQuotInt0(Succ(vuz1850), Succ(vuz1990), vuz144) -> new_primQuotInt0(vuz1850, vuz1990, vuz144) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (423) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_primQuotInt0(Succ(vuz1850), Succ(vuz1990), vuz144) -> new_primQuotInt0(vuz1850, vuz1990, vuz144) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 ---------------------------------------- (424) YES ---------------------------------------- (425) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMinusNatS(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS(vuz3380, vuz3390) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (426) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_primMinusNatS(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS(vuz3380, vuz3390) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (427) YES ---------------------------------------- (428) Obligation: Q DP problem: The TRS P consists of the following rules: new_primPlusNat(Succ(vuz6600), Succ(vuz41000)) -> new_primPlusNat(vuz6600, vuz41000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (429) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_primPlusNat(Succ(vuz6600), Succ(vuz41000)) -> new_primPlusNat(vuz6600, vuz41000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (430) YES ---------------------------------------- (431) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd20(Succ(vuz3500), Succ(vuz3660), vuz144) -> new_gcd20(vuz3500, vuz3660, vuz144) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (432) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_gcd20(Succ(vuz3500), Succ(vuz3660), vuz144) -> new_gcd20(vuz3500, vuz3660, vuz144) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 ---------------------------------------- (433) YES ---------------------------------------- (434) Narrow (COMPLETE) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="(-)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="(-) vuz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="(-) vuz3 vuz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="vuz3 + (negate vuz4)",fontsize=16,color="burlywood",shape="box"];6382[label="vuz3/vuz30 :% vuz31",fontsize=10,color="white",style="solid",shape="box"];5 -> 6382[label="",style="solid", color="burlywood", weight=9]; 6382 -> 6[label="",style="solid", color="burlywood", weight=3]; 6[label="vuz30 :% vuz31 + (negate vuz4)",fontsize=16,color="burlywood",shape="box"];6383[label="vuz4/vuz40 :% vuz41",fontsize=10,color="white",style="solid",shape="box"];6 -> 6383[label="",style="solid", color="burlywood", weight=9]; 6383 -> 7[label="",style="solid", color="burlywood", weight=3]; 7[label="vuz30 :% vuz31 + (negate vuz40 :% vuz41)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 8[label="vuz30 :% vuz31 + (negate vuz40) :% vuz41",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 9[label="vuz30 :% vuz31 + primNegInt vuz40 :% vuz41",fontsize=16,color="burlywood",shape="box"];6384[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];9 -> 6384[label="",style="solid", color="burlywood", weight=9]; 6384 -> 10[label="",style="solid", color="burlywood", weight=3]; 6385[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];9 -> 6385[label="",style="solid", color="burlywood", weight=9]; 6385 -> 11[label="",style="solid", color="burlywood", weight=3]; 10[label="vuz30 :% vuz31 + primNegInt (Pos vuz400) :% vuz41",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3]; 11[label="vuz30 :% vuz31 + primNegInt (Neg vuz400) :% vuz41",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3]; 12[label="vuz30 :% vuz31 + Neg vuz400 :% vuz41",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3]; 13[label="vuz30 :% vuz31 + Pos vuz400 :% vuz41",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3]; 14[label="reduce (vuz30 * vuz41 + Neg vuz400 * vuz31) (vuz31 * vuz41)",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3]; 15[label="reduce (vuz30 * vuz41 + Pos vuz400 * vuz31) (vuz31 * vuz41)",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 16[label="reduce2 (vuz30 * vuz41 + Neg vuz400 * vuz31) (vuz31 * vuz41)",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3]; 17[label="reduce2 (vuz30 * vuz41 + Pos vuz400 * vuz31) (vuz31 * vuz41)",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3]; 18[label="reduce2Reduce1 (vuz30 * vuz41 + Neg vuz400 * vuz31) (vuz31 * vuz41) (vuz30 * vuz41 + Neg vuz400 * vuz31) (vuz31 * vuz41) (vuz31 * vuz41 == fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3]; 19[label="reduce2Reduce1 (vuz30 * vuz41 + Pos vuz400 * vuz31) (vuz31 * vuz41) (vuz30 * vuz41 + Pos vuz400 * vuz31) (vuz31 * vuz41) (vuz31 * vuz41 == fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3]; 20[label="reduce2Reduce1 (vuz30 * vuz41 + Neg vuz400 * vuz31) (vuz31 * vuz41) (vuz30 * vuz41 + Neg vuz400 * vuz31) (vuz31 * vuz41) (primEqInt (vuz31 * vuz41) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3]; 21[label="reduce2Reduce1 (vuz30 * vuz41 + Pos vuz400 * vuz31) (vuz31 * vuz41) (vuz30 * vuz41 + Pos vuz400 * vuz31) (vuz31 * vuz41) (primEqInt (vuz31 * vuz41) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3]; 22[label="reduce2Reduce1 (vuz30 * vuz41 + Neg vuz400 * vuz31) (primMulInt vuz31 vuz41) (vuz30 * vuz41 + Neg vuz400 * vuz31) (primMulInt vuz31 vuz41) (primEqInt (primMulInt vuz31 vuz41) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6386[label="vuz31/Pos vuz310",fontsize=10,color="white",style="solid",shape="box"];22 -> 6386[label="",style="solid", color="burlywood", weight=9]; 6386 -> 24[label="",style="solid", color="burlywood", weight=3]; 6387[label="vuz31/Neg vuz310",fontsize=10,color="white",style="solid",shape="box"];22 -> 6387[label="",style="solid", color="burlywood", weight=9]; 6387 -> 25[label="",style="solid", color="burlywood", weight=3]; 23[label="reduce2Reduce1 (vuz30 * vuz41 + Pos vuz400 * vuz31) (primMulInt vuz31 vuz41) (vuz30 * vuz41 + Pos vuz400 * vuz31) (primMulInt vuz31 vuz41) (primEqInt (primMulInt vuz31 vuz41) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6388[label="vuz31/Pos vuz310",fontsize=10,color="white",style="solid",shape="box"];23 -> 6388[label="",style="solid", color="burlywood", weight=9]; 6388 -> 26[label="",style="solid", color="burlywood", weight=3]; 6389[label="vuz31/Neg vuz310",fontsize=10,color="white",style="solid",shape="box"];23 -> 6389[label="",style="solid", color="burlywood", weight=9]; 6389 -> 27[label="",style="solid", color="burlywood", weight=3]; 24[label="reduce2Reduce1 (vuz30 * vuz41 + Neg vuz400 * Pos vuz310) (primMulInt (Pos vuz310) vuz41) (vuz30 * vuz41 + Neg vuz400 * Pos vuz310) (primMulInt (Pos vuz310) vuz41) (primEqInt (primMulInt (Pos vuz310) vuz41) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6390[label="vuz41/Pos vuz410",fontsize=10,color="white",style="solid",shape="box"];24 -> 6390[label="",style="solid", color="burlywood", weight=9]; 6390 -> 28[label="",style="solid", color="burlywood", weight=3]; 6391[label="vuz41/Neg vuz410",fontsize=10,color="white",style="solid",shape="box"];24 -> 6391[label="",style="solid", color="burlywood", weight=9]; 6391 -> 29[label="",style="solid", color="burlywood", weight=3]; 25[label="reduce2Reduce1 (vuz30 * vuz41 + Neg vuz400 * Neg vuz310) (primMulInt (Neg vuz310) vuz41) (vuz30 * vuz41 + Neg vuz400 * Neg vuz310) (primMulInt (Neg vuz310) vuz41) (primEqInt (primMulInt (Neg vuz310) vuz41) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6392[label="vuz41/Pos vuz410",fontsize=10,color="white",style="solid",shape="box"];25 -> 6392[label="",style="solid", color="burlywood", weight=9]; 6392 -> 30[label="",style="solid", color="burlywood", weight=3]; 6393[label="vuz41/Neg vuz410",fontsize=10,color="white",style="solid",shape="box"];25 -> 6393[label="",style="solid", color="burlywood", weight=9]; 6393 -> 31[label="",style="solid", color="burlywood", weight=3]; 26[label="reduce2Reduce1 (vuz30 * vuz41 + Pos vuz400 * Pos vuz310) (primMulInt (Pos vuz310) vuz41) (vuz30 * vuz41 + Pos vuz400 * Pos vuz310) (primMulInt (Pos vuz310) vuz41) (primEqInt (primMulInt (Pos vuz310) vuz41) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6394[label="vuz41/Pos vuz410",fontsize=10,color="white",style="solid",shape="box"];26 -> 6394[label="",style="solid", color="burlywood", weight=9]; 6394 -> 32[label="",style="solid", color="burlywood", weight=3]; 6395[label="vuz41/Neg vuz410",fontsize=10,color="white",style="solid",shape="box"];26 -> 6395[label="",style="solid", color="burlywood", weight=9]; 6395 -> 33[label="",style="solid", color="burlywood", weight=3]; 27[label="reduce2Reduce1 (vuz30 * vuz41 + Pos vuz400 * Neg vuz310) (primMulInt (Neg vuz310) vuz41) (vuz30 * vuz41 + Pos vuz400 * Neg vuz310) (primMulInt (Neg vuz310) vuz41) (primEqInt (primMulInt (Neg vuz310) vuz41) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6396[label="vuz41/Pos vuz410",fontsize=10,color="white",style="solid",shape="box"];27 -> 6396[label="",style="solid", color="burlywood", weight=9]; 6396 -> 34[label="",style="solid", color="burlywood", weight=3]; 6397[label="vuz41/Neg vuz410",fontsize=10,color="white",style="solid",shape="box"];27 -> 6397[label="",style="solid", color="burlywood", weight=9]; 6397 -> 35[label="",style="solid", color="burlywood", weight=3]; 28[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Neg vuz400 * Pos vuz310) (primMulInt (Pos vuz310) (Pos vuz410)) (vuz30 * Pos vuz410 + Neg vuz400 * Pos vuz310) (primMulInt (Pos vuz310) (Pos vuz410)) (primEqInt (primMulInt (Pos vuz310) (Pos vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];28 -> 36[label="",style="solid", color="black", weight=3]; 29[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Neg vuz400 * Pos vuz310) (primMulInt (Pos vuz310) (Neg vuz410)) (vuz30 * Neg vuz410 + Neg vuz400 * Pos vuz310) (primMulInt (Pos vuz310) (Neg vuz410)) (primEqInt (primMulInt (Pos vuz310) (Neg vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];29 -> 37[label="",style="solid", color="black", weight=3]; 30[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Neg vuz400 * Neg vuz310) (primMulInt (Neg vuz310) (Pos vuz410)) (vuz30 * Pos vuz410 + Neg vuz400 * Neg vuz310) (primMulInt (Neg vuz310) (Pos vuz410)) (primEqInt (primMulInt (Neg vuz310) (Pos vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];30 -> 38[label="",style="solid", color="black", weight=3]; 31[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Neg vuz400 * Neg vuz310) (primMulInt (Neg vuz310) (Neg vuz410)) (vuz30 * Neg vuz410 + Neg vuz400 * Neg vuz310) (primMulInt (Neg vuz310) (Neg vuz410)) (primEqInt (primMulInt (Neg vuz310) (Neg vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];31 -> 39[label="",style="solid", color="black", weight=3]; 32[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Pos vuz400 * Pos vuz310) (primMulInt (Pos vuz310) (Pos vuz410)) (vuz30 * Pos vuz410 + Pos vuz400 * Pos vuz310) (primMulInt (Pos vuz310) (Pos vuz410)) (primEqInt (primMulInt (Pos vuz310) (Pos vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];32 -> 40[label="",style="solid", color="black", weight=3]; 33[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Pos vuz400 * Pos vuz310) (primMulInt (Pos vuz310) (Neg vuz410)) (vuz30 * Neg vuz410 + Pos vuz400 * Pos vuz310) (primMulInt (Pos vuz310) (Neg vuz410)) (primEqInt (primMulInt (Pos vuz310) (Neg vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];33 -> 41[label="",style="solid", color="black", weight=3]; 34[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Pos vuz400 * Neg vuz310) (primMulInt (Neg vuz310) (Pos vuz410)) (vuz30 * Pos vuz410 + Pos vuz400 * Neg vuz310) (primMulInt (Neg vuz310) (Pos vuz410)) (primEqInt (primMulInt (Neg vuz310) (Pos vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];34 -> 42[label="",style="solid", color="black", weight=3]; 35[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Pos vuz400 * Neg vuz310) (primMulInt (Neg vuz310) (Neg vuz410)) (vuz30 * Neg vuz410 + Pos vuz400 * Neg vuz310) (primMulInt (Neg vuz310) (Neg vuz410)) (primEqInt (primMulInt (Neg vuz310) (Neg vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];35 -> 43[label="",style="solid", color="black", weight=3]; 36[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Neg vuz400 * Pos vuz310) (Pos (primMulNat vuz310 vuz410)) (vuz30 * Pos vuz410 + Neg vuz400 * Pos vuz310) (Pos (primMulNat vuz310 vuz410)) (primEqInt (Pos (primMulNat vuz310 vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6398[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];36 -> 6398[label="",style="solid", color="burlywood", weight=9]; 6398 -> 44[label="",style="solid", color="burlywood", weight=3]; 6399[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];36 -> 6399[label="",style="solid", color="burlywood", weight=9]; 6399 -> 45[label="",style="solid", color="burlywood", weight=3]; 37[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Neg vuz400 * Pos vuz310) (Neg (primMulNat vuz310 vuz410)) (vuz30 * Neg vuz410 + Neg vuz400 * Pos vuz310) (Neg (primMulNat vuz310 vuz410)) (primEqInt (Neg (primMulNat vuz310 vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6400[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];37 -> 6400[label="",style="solid", color="burlywood", weight=9]; 6400 -> 46[label="",style="solid", color="burlywood", weight=3]; 6401[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];37 -> 6401[label="",style="solid", color="burlywood", weight=9]; 6401 -> 47[label="",style="solid", color="burlywood", weight=3]; 38[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Neg vuz400 * Neg vuz310) (Neg (primMulNat vuz310 vuz410)) (vuz30 * Pos vuz410 + Neg vuz400 * Neg vuz310) (Neg (primMulNat vuz310 vuz410)) (primEqInt (Neg (primMulNat vuz310 vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6402[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];38 -> 6402[label="",style="solid", color="burlywood", weight=9]; 6402 -> 48[label="",style="solid", color="burlywood", weight=3]; 6403[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];38 -> 6403[label="",style="solid", color="burlywood", weight=9]; 6403 -> 49[label="",style="solid", color="burlywood", weight=3]; 39[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Neg vuz400 * Neg vuz310) (Pos (primMulNat vuz310 vuz410)) (vuz30 * Neg vuz410 + Neg vuz400 * Neg vuz310) (Pos (primMulNat vuz310 vuz410)) (primEqInt (Pos (primMulNat vuz310 vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6404[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];39 -> 6404[label="",style="solid", color="burlywood", weight=9]; 6404 -> 50[label="",style="solid", color="burlywood", weight=3]; 6405[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];39 -> 6405[label="",style="solid", color="burlywood", weight=9]; 6405 -> 51[label="",style="solid", color="burlywood", weight=3]; 40[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Pos vuz400 * Pos vuz310) (Pos (primMulNat vuz310 vuz410)) (vuz30 * Pos vuz410 + Pos vuz400 * Pos vuz310) (Pos (primMulNat vuz310 vuz410)) (primEqInt (Pos (primMulNat vuz310 vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6406[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];40 -> 6406[label="",style="solid", color="burlywood", weight=9]; 6406 -> 52[label="",style="solid", color="burlywood", weight=3]; 6407[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];40 -> 6407[label="",style="solid", color="burlywood", weight=9]; 6407 -> 53[label="",style="solid", color="burlywood", weight=3]; 41[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Pos vuz400 * Pos vuz310) (Neg (primMulNat vuz310 vuz410)) (vuz30 * Neg vuz410 + Pos vuz400 * Pos vuz310) (Neg (primMulNat vuz310 vuz410)) (primEqInt (Neg (primMulNat vuz310 vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6408[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];41 -> 6408[label="",style="solid", color="burlywood", weight=9]; 6408 -> 54[label="",style="solid", color="burlywood", weight=3]; 6409[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];41 -> 6409[label="",style="solid", color="burlywood", weight=9]; 6409 -> 55[label="",style="solid", color="burlywood", weight=3]; 42[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Pos vuz400 * Neg vuz310) (Neg (primMulNat vuz310 vuz410)) (vuz30 * Pos vuz410 + Pos vuz400 * Neg vuz310) (Neg (primMulNat vuz310 vuz410)) (primEqInt (Neg (primMulNat vuz310 vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6410[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];42 -> 6410[label="",style="solid", color="burlywood", weight=9]; 6410 -> 56[label="",style="solid", color="burlywood", weight=3]; 6411[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];42 -> 6411[label="",style="solid", color="burlywood", weight=9]; 6411 -> 57[label="",style="solid", color="burlywood", weight=3]; 43[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Pos vuz400 * Neg vuz310) (Pos (primMulNat vuz310 vuz410)) (vuz30 * Neg vuz410 + Pos vuz400 * Neg vuz310) (Pos (primMulNat vuz310 vuz410)) (primEqInt (Pos (primMulNat vuz310 vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6412[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];43 -> 6412[label="",style="solid", color="burlywood", weight=9]; 6412 -> 58[label="",style="solid", color="burlywood", weight=3]; 6413[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];43 -> 6413[label="",style="solid", color="burlywood", weight=9]; 6413 -> 59[label="",style="solid", color="burlywood", weight=3]; 44[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Neg vuz400 * Pos (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) vuz410)) (vuz30 * Pos vuz410 + Neg vuz400 * Pos (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) vuz410)) (primEqInt (Pos (primMulNat (Succ vuz3100) vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6414[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];44 -> 6414[label="",style="solid", color="burlywood", weight=9]; 6414 -> 60[label="",style="solid", color="burlywood", weight=3]; 6415[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];44 -> 6415[label="",style="solid", color="burlywood", weight=9]; 6415 -> 61[label="",style="solid", color="burlywood", weight=3]; 45[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Neg vuz400 * Pos Zero) (Pos (primMulNat Zero vuz410)) (vuz30 * Pos vuz410 + Neg vuz400 * Pos Zero) (Pos (primMulNat Zero vuz410)) (primEqInt (Pos (primMulNat Zero vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6416[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];45 -> 6416[label="",style="solid", color="burlywood", weight=9]; 6416 -> 62[label="",style="solid", color="burlywood", weight=3]; 6417[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];45 -> 6417[label="",style="solid", color="burlywood", weight=9]; 6417 -> 63[label="",style="solid", color="burlywood", weight=3]; 46[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Neg vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) vuz410)) (vuz30 * Neg vuz410 + Neg vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) vuz410)) (primEqInt (Neg (primMulNat (Succ vuz3100) vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6418[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];46 -> 6418[label="",style="solid", color="burlywood", weight=9]; 6418 -> 64[label="",style="solid", color="burlywood", weight=3]; 6419[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];46 -> 6419[label="",style="solid", color="burlywood", weight=9]; 6419 -> 65[label="",style="solid", color="burlywood", weight=3]; 47[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Neg vuz400 * Pos Zero) (Neg (primMulNat Zero vuz410)) (vuz30 * Neg vuz410 + Neg vuz400 * Pos Zero) (Neg (primMulNat Zero vuz410)) (primEqInt (Neg (primMulNat Zero vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6420[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];47 -> 6420[label="",style="solid", color="burlywood", weight=9]; 6420 -> 66[label="",style="solid", color="burlywood", weight=3]; 6421[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];47 -> 6421[label="",style="solid", color="burlywood", weight=9]; 6421 -> 67[label="",style="solid", color="burlywood", weight=3]; 48[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Neg vuz400 * Neg (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) vuz410)) (vuz30 * Pos vuz410 + Neg vuz400 * Neg (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) vuz410)) (primEqInt (Neg (primMulNat (Succ vuz3100) vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6422[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];48 -> 6422[label="",style="solid", color="burlywood", weight=9]; 6422 -> 68[label="",style="solid", color="burlywood", weight=3]; 6423[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];48 -> 6423[label="",style="solid", color="burlywood", weight=9]; 6423 -> 69[label="",style="solid", color="burlywood", weight=3]; 49[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Neg vuz400 * Neg Zero) (Neg (primMulNat Zero vuz410)) (vuz30 * Pos vuz410 + Neg vuz400 * Neg Zero) (Neg (primMulNat Zero vuz410)) (primEqInt (Neg (primMulNat Zero vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6424[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];49 -> 6424[label="",style="solid", color="burlywood", weight=9]; 6424 -> 70[label="",style="solid", color="burlywood", weight=3]; 6425[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];49 -> 6425[label="",style="solid", color="burlywood", weight=9]; 6425 -> 71[label="",style="solid", color="burlywood", weight=3]; 50[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Neg vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) vuz410)) (vuz30 * Neg vuz410 + Neg vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) vuz410)) (primEqInt (Pos (primMulNat (Succ vuz3100) vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6426[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];50 -> 6426[label="",style="solid", color="burlywood", weight=9]; 6426 -> 72[label="",style="solid", color="burlywood", weight=3]; 6427[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];50 -> 6427[label="",style="solid", color="burlywood", weight=9]; 6427 -> 73[label="",style="solid", color="burlywood", weight=3]; 51[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Neg vuz400 * Neg Zero) (Pos (primMulNat Zero vuz410)) (vuz30 * Neg vuz410 + Neg vuz400 * Neg Zero) (Pos (primMulNat Zero vuz410)) (primEqInt (Pos (primMulNat Zero vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6428[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];51 -> 6428[label="",style="solid", color="burlywood", weight=9]; 6428 -> 74[label="",style="solid", color="burlywood", weight=3]; 6429[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];51 -> 6429[label="",style="solid", color="burlywood", weight=9]; 6429 -> 75[label="",style="solid", color="burlywood", weight=3]; 52[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Pos vuz400 * Pos (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) vuz410)) (vuz30 * Pos vuz410 + Pos vuz400 * Pos (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) vuz410)) (primEqInt (Pos (primMulNat (Succ vuz3100) vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6430[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];52 -> 6430[label="",style="solid", color="burlywood", weight=9]; 6430 -> 76[label="",style="solid", color="burlywood", weight=3]; 6431[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];52 -> 6431[label="",style="solid", color="burlywood", weight=9]; 6431 -> 77[label="",style="solid", color="burlywood", weight=3]; 53[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Pos vuz400 * Pos Zero) (Pos (primMulNat Zero vuz410)) (vuz30 * Pos vuz410 + Pos vuz400 * Pos Zero) (Pos (primMulNat Zero vuz410)) (primEqInt (Pos (primMulNat Zero vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6432[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];53 -> 6432[label="",style="solid", color="burlywood", weight=9]; 6432 -> 78[label="",style="solid", color="burlywood", weight=3]; 6433[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];53 -> 6433[label="",style="solid", color="burlywood", weight=9]; 6433 -> 79[label="",style="solid", color="burlywood", weight=3]; 54[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Pos vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) vuz410)) (vuz30 * Neg vuz410 + Pos vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) vuz410)) (primEqInt (Neg (primMulNat (Succ vuz3100) vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6434[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];54 -> 6434[label="",style="solid", color="burlywood", weight=9]; 6434 -> 80[label="",style="solid", color="burlywood", weight=3]; 6435[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];54 -> 6435[label="",style="solid", color="burlywood", weight=9]; 6435 -> 81[label="",style="solid", color="burlywood", weight=3]; 55[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Pos vuz400 * Pos Zero) (Neg (primMulNat Zero vuz410)) (vuz30 * Neg vuz410 + Pos vuz400 * Pos Zero) (Neg (primMulNat Zero vuz410)) (primEqInt (Neg (primMulNat Zero vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6436[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];55 -> 6436[label="",style="solid", color="burlywood", weight=9]; 6436 -> 82[label="",style="solid", color="burlywood", weight=3]; 6437[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];55 -> 6437[label="",style="solid", color="burlywood", weight=9]; 6437 -> 83[label="",style="solid", color="burlywood", weight=3]; 56[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Pos vuz400 * Neg (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) vuz410)) (vuz30 * Pos vuz410 + Pos vuz400 * Neg (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) vuz410)) (primEqInt (Neg (primMulNat (Succ vuz3100) vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6438[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];56 -> 6438[label="",style="solid", color="burlywood", weight=9]; 6438 -> 84[label="",style="solid", color="burlywood", weight=3]; 6439[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];56 -> 6439[label="",style="solid", color="burlywood", weight=9]; 6439 -> 85[label="",style="solid", color="burlywood", weight=3]; 57[label="reduce2Reduce1 (vuz30 * Pos vuz410 + Pos vuz400 * Neg Zero) (Neg (primMulNat Zero vuz410)) (vuz30 * Pos vuz410 + Pos vuz400 * Neg Zero) (Neg (primMulNat Zero vuz410)) (primEqInt (Neg (primMulNat Zero vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6440[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];57 -> 6440[label="",style="solid", color="burlywood", weight=9]; 6440 -> 86[label="",style="solid", color="burlywood", weight=3]; 6441[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];57 -> 6441[label="",style="solid", color="burlywood", weight=9]; 6441 -> 87[label="",style="solid", color="burlywood", weight=3]; 58[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Pos vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) vuz410)) (vuz30 * Neg vuz410 + Pos vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) vuz410)) (primEqInt (Pos (primMulNat (Succ vuz3100) vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6442[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];58 -> 6442[label="",style="solid", color="burlywood", weight=9]; 6442 -> 88[label="",style="solid", color="burlywood", weight=3]; 6443[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];58 -> 6443[label="",style="solid", color="burlywood", weight=9]; 6443 -> 89[label="",style="solid", color="burlywood", weight=3]; 59[label="reduce2Reduce1 (vuz30 * Neg vuz410 + Pos vuz400 * Neg Zero) (Pos (primMulNat Zero vuz410)) (vuz30 * Neg vuz410 + Pos vuz400 * Neg Zero) (Pos (primMulNat Zero vuz410)) (primEqInt (Pos (primMulNat Zero vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6444[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];59 -> 6444[label="",style="solid", color="burlywood", weight=9]; 6444 -> 90[label="",style="solid", color="burlywood", weight=3]; 6445[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];59 -> 6445[label="",style="solid", color="burlywood", weight=9]; 6445 -> 91[label="",style="solid", color="burlywood", weight=3]; 60[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) (Succ vuz4100))) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) (Succ vuz4100))) (primEqInt (Pos (primMulNat (Succ vuz3100) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];60 -> 92[label="",style="solid", color="black", weight=3]; 61[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Pos (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) Zero)) (vuz30 * Pos Zero + Neg vuz400 * Pos (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) Zero)) (primEqInt (Pos (primMulNat (Succ vuz3100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];61 -> 93[label="",style="solid", color="black", weight=3]; 62[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos Zero) (Pos (primMulNat Zero (Succ vuz4100))) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos Zero) (Pos (primMulNat Zero (Succ vuz4100))) (primEqInt (Pos (primMulNat Zero (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];62 -> 94[label="",style="solid", color="black", weight=3]; 63[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Pos Zero) (Pos (primMulNat Zero Zero)) (vuz30 * Pos Zero + Neg vuz400 * Pos Zero) (Pos (primMulNat Zero Zero)) (primEqInt (Pos (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];63 -> 95[label="",style="solid", color="black", weight=3]; 64[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) (Succ vuz4100))) (primEqInt (Neg (primMulNat (Succ vuz3100) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];64 -> 96[label="",style="solid", color="black", weight=3]; 65[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) Zero)) (vuz30 * Neg Zero + Neg vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) Zero)) (primEqInt (Neg (primMulNat (Succ vuz3100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];65 -> 97[label="",style="solid", color="black", weight=3]; 66[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos Zero) (Neg (primMulNat Zero (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos Zero) (Neg (primMulNat Zero (Succ vuz4100))) (primEqInt (Neg (primMulNat Zero (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];66 -> 98[label="",style="solid", color="black", weight=3]; 67[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Pos Zero) (Neg (primMulNat Zero Zero)) (vuz30 * Neg Zero + Neg vuz400 * Pos Zero) (Neg (primMulNat Zero Zero)) (primEqInt (Neg (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];67 -> 99[label="",style="solid", color="black", weight=3]; 68[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) (Succ vuz4100))) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) (Succ vuz4100))) (primEqInt (Neg (primMulNat (Succ vuz3100) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];68 -> 100[label="",style="solid", color="black", weight=3]; 69[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Neg (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) Zero)) (vuz30 * Pos Zero + Neg vuz400 * Neg (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) Zero)) (primEqInt (Neg (primMulNat (Succ vuz3100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];69 -> 101[label="",style="solid", color="black", weight=3]; 70[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg Zero) (Neg (primMulNat Zero (Succ vuz4100))) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg Zero) (Neg (primMulNat Zero (Succ vuz4100))) (primEqInt (Neg (primMulNat Zero (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];70 -> 102[label="",style="solid", color="black", weight=3]; 71[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Neg Zero) (Neg (primMulNat Zero Zero)) (vuz30 * Pos Zero + Neg vuz400 * Neg Zero) (Neg (primMulNat Zero Zero)) (primEqInt (Neg (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];71 -> 103[label="",style="solid", color="black", weight=3]; 72[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) (Succ vuz4100))) (primEqInt (Pos (primMulNat (Succ vuz3100) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];72 -> 104[label="",style="solid", color="black", weight=3]; 73[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) Zero)) (vuz30 * Neg Zero + Neg vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) Zero)) (primEqInt (Pos (primMulNat (Succ vuz3100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];73 -> 105[label="",style="solid", color="black", weight=3]; 74[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg Zero) (Pos (primMulNat Zero (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg Zero) (Pos (primMulNat Zero (Succ vuz4100))) (primEqInt (Pos (primMulNat Zero (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];74 -> 106[label="",style="solid", color="black", weight=3]; 75[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Neg Zero) (Pos (primMulNat Zero Zero)) (vuz30 * Neg Zero + Neg vuz400 * Neg Zero) (Pos (primMulNat Zero Zero)) (primEqInt (Pos (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];75 -> 107[label="",style="solid", color="black", weight=3]; 76[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) (Succ vuz4100))) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) (Succ vuz4100))) (primEqInt (Pos (primMulNat (Succ vuz3100) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];76 -> 108[label="",style="solid", color="black", weight=3]; 77[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Pos (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) Zero)) (vuz30 * Pos Zero + Pos vuz400 * Pos (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) Zero)) (primEqInt (Pos (primMulNat (Succ vuz3100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];77 -> 109[label="",style="solid", color="black", weight=3]; 78[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos Zero) (Pos (primMulNat Zero (Succ vuz4100))) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos Zero) (Pos (primMulNat Zero (Succ vuz4100))) (primEqInt (Pos (primMulNat Zero (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];78 -> 110[label="",style="solid", color="black", weight=3]; 79[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Pos Zero) (Pos (primMulNat Zero Zero)) (vuz30 * Pos Zero + Pos vuz400 * Pos Zero) (Pos (primMulNat Zero Zero)) (primEqInt (Pos (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];79 -> 111[label="",style="solid", color="black", weight=3]; 80[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) (Succ vuz4100))) (primEqInt (Neg (primMulNat (Succ vuz3100) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];80 -> 112[label="",style="solid", color="black", weight=3]; 81[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) Zero)) (vuz30 * Neg Zero + Pos vuz400 * Pos (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) Zero)) (primEqInt (Neg (primMulNat (Succ vuz3100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];81 -> 113[label="",style="solid", color="black", weight=3]; 82[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos Zero) (Neg (primMulNat Zero (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos Zero) (Neg (primMulNat Zero (Succ vuz4100))) (primEqInt (Neg (primMulNat Zero (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];82 -> 114[label="",style="solid", color="black", weight=3]; 83[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Pos Zero) (Neg (primMulNat Zero Zero)) (vuz30 * Neg Zero + Pos vuz400 * Pos Zero) (Neg (primMulNat Zero Zero)) (primEqInt (Neg (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];83 -> 115[label="",style="solid", color="black", weight=3]; 84[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) (Succ vuz4100))) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) (Succ vuz4100))) (primEqInt (Neg (primMulNat (Succ vuz3100) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];84 -> 116[label="",style="solid", color="black", weight=3]; 85[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Neg (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) Zero)) (vuz30 * Pos Zero + Pos vuz400 * Neg (Succ vuz3100)) (Neg (primMulNat (Succ vuz3100) Zero)) (primEqInt (Neg (primMulNat (Succ vuz3100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];85 -> 117[label="",style="solid", color="black", weight=3]; 86[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg Zero) (Neg (primMulNat Zero (Succ vuz4100))) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg Zero) (Neg (primMulNat Zero (Succ vuz4100))) (primEqInt (Neg (primMulNat Zero (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];86 -> 118[label="",style="solid", color="black", weight=3]; 87[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Neg Zero) (Neg (primMulNat Zero Zero)) (vuz30 * Pos Zero + Pos vuz400 * Neg Zero) (Neg (primMulNat Zero Zero)) (primEqInt (Neg (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];87 -> 119[label="",style="solid", color="black", weight=3]; 88[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) (Succ vuz4100))) (primEqInt (Pos (primMulNat (Succ vuz3100) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];88 -> 120[label="",style="solid", color="black", weight=3]; 89[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) Zero)) (vuz30 * Neg Zero + Pos vuz400 * Neg (Succ vuz3100)) (Pos (primMulNat (Succ vuz3100) Zero)) (primEqInt (Pos (primMulNat (Succ vuz3100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];89 -> 121[label="",style="solid", color="black", weight=3]; 90[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg Zero) (Pos (primMulNat Zero (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg Zero) (Pos (primMulNat Zero (Succ vuz4100))) (primEqInt (Pos (primMulNat Zero (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];90 -> 122[label="",style="solid", color="black", weight=3]; 91[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Neg Zero) (Pos (primMulNat Zero Zero)) (vuz30 * Neg Zero + Pos vuz400 * Neg Zero) (Pos (primMulNat Zero Zero)) (primEqInt (Pos (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];91 -> 123[label="",style="solid", color="black", weight=3]; 92 -> 1963[label="",style="dashed", color="red", weight=0]; 92[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos (Succ vuz3100)) (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos (Succ vuz3100)) (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (primEqInt (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];92 -> 1964[label="",style="dashed", color="magenta", weight=3]; 92 -> 1965[label="",style="dashed", color="magenta", weight=3]; 92 -> 1966[label="",style="dashed", color="magenta", weight=3]; 92 -> 1967[label="",style="dashed", color="magenta", weight=3]; 92 -> 1968[label="",style="dashed", color="magenta", weight=3]; 92 -> 1969[label="",style="dashed", color="magenta", weight=3]; 92 -> 1970[label="",style="dashed", color="magenta", weight=3]; 93[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Pos (Succ vuz3100)) (Pos Zero) (vuz30 * Pos Zero + Neg vuz400 * Pos (Succ vuz3100)) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];93 -> 126[label="",style="solid", color="black", weight=3]; 94[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];94 -> 127[label="",style="solid", color="black", weight=3]; 95[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos Zero + Neg vuz400 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];95 -> 128[label="",style="solid", color="black", weight=3]; 96 -> 1030[label="",style="dashed", color="red", weight=0]; 96[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos (Succ vuz3100)) (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos (Succ vuz3100)) (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (primEqInt (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];96 -> 1031[label="",style="dashed", color="magenta", weight=3]; 96 -> 1032[label="",style="dashed", color="magenta", weight=3]; 96 -> 1033[label="",style="dashed", color="magenta", weight=3]; 96 -> 1034[label="",style="dashed", color="magenta", weight=3]; 96 -> 1035[label="",style="dashed", color="magenta", weight=3]; 96 -> 1036[label="",style="dashed", color="magenta", weight=3]; 96 -> 1037[label="",style="dashed", color="magenta", weight=3]; 97[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Pos (Succ vuz3100)) (Neg Zero) (vuz30 * Neg Zero + Neg vuz400 * Pos (Succ vuz3100)) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];97 -> 131[label="",style="solid", color="black", weight=3]; 98[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];98 -> 132[label="",style="solid", color="black", weight=3]; 99[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg Zero + Neg vuz400 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];99 -> 133[label="",style="solid", color="black", weight=3]; 100 -> 1073[label="",style="dashed", color="red", weight=0]; 100[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg (Succ vuz3100)) (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg (Succ vuz3100)) (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (primEqInt (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];100 -> 1074[label="",style="dashed", color="magenta", weight=3]; 100 -> 1075[label="",style="dashed", color="magenta", weight=3]; 100 -> 1076[label="",style="dashed", color="magenta", weight=3]; 100 -> 1077[label="",style="dashed", color="magenta", weight=3]; 100 -> 1078[label="",style="dashed", color="magenta", weight=3]; 100 -> 1079[label="",style="dashed", color="magenta", weight=3]; 100 -> 1080[label="",style="dashed", color="magenta", weight=3]; 101[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Neg (Succ vuz3100)) (Neg Zero) (vuz30 * Pos Zero + Neg vuz400 * Neg (Succ vuz3100)) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];101 -> 136[label="",style="solid", color="black", weight=3]; 102[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];102 -> 137[label="",style="solid", color="black", weight=3]; 103[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos Zero + Neg vuz400 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];103 -> 138[label="",style="solid", color="black", weight=3]; 104 -> 1126[label="",style="dashed", color="red", weight=0]; 104[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg (Succ vuz3100)) (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg (Succ vuz3100)) (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (primEqInt (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];104 -> 1127[label="",style="dashed", color="magenta", weight=3]; 104 -> 1128[label="",style="dashed", color="magenta", weight=3]; 104 -> 1129[label="",style="dashed", color="magenta", weight=3]; 104 -> 1130[label="",style="dashed", color="magenta", weight=3]; 104 -> 1131[label="",style="dashed", color="magenta", weight=3]; 104 -> 1132[label="",style="dashed", color="magenta", weight=3]; 104 -> 1133[label="",style="dashed", color="magenta", weight=3]; 105[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Neg (Succ vuz3100)) (Pos Zero) (vuz30 * Neg Zero + Neg vuz400 * Neg (Succ vuz3100)) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];105 -> 141[label="",style="solid", color="black", weight=3]; 106[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];106 -> 142[label="",style="solid", color="black", weight=3]; 107[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg Zero + Neg vuz400 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];107 -> 143[label="",style="solid", color="black", weight=3]; 108 -> 1186[label="",style="dashed", color="red", weight=0]; 108[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos (Succ vuz3100)) (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos (Succ vuz3100)) (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (primEqInt (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];108 -> 1187[label="",style="dashed", color="magenta", weight=3]; 108 -> 1188[label="",style="dashed", color="magenta", weight=3]; 108 -> 1189[label="",style="dashed", color="magenta", weight=3]; 108 -> 1190[label="",style="dashed", color="magenta", weight=3]; 108 -> 1191[label="",style="dashed", color="magenta", weight=3]; 108 -> 1192[label="",style="dashed", color="magenta", weight=3]; 108 -> 1193[label="",style="dashed", color="magenta", weight=3]; 109[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Pos (Succ vuz3100)) (Pos Zero) (vuz30 * Pos Zero + Pos vuz400 * Pos (Succ vuz3100)) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];109 -> 146[label="",style="solid", color="black", weight=3]; 110[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];110 -> 147[label="",style="solid", color="black", weight=3]; 111[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos Zero + Pos vuz400 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];111 -> 148[label="",style="solid", color="black", weight=3]; 112 -> 1359[label="",style="dashed", color="red", weight=0]; 112[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos (Succ vuz3100)) (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos (Succ vuz3100)) (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (primEqInt (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];112 -> 1360[label="",style="dashed", color="magenta", weight=3]; 112 -> 1361[label="",style="dashed", color="magenta", weight=3]; 112 -> 1362[label="",style="dashed", color="magenta", weight=3]; 112 -> 1363[label="",style="dashed", color="magenta", weight=3]; 112 -> 1364[label="",style="dashed", color="magenta", weight=3]; 112 -> 1365[label="",style="dashed", color="magenta", weight=3]; 112 -> 1366[label="",style="dashed", color="magenta", weight=3]; 113[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Pos (Succ vuz3100)) (Neg Zero) (vuz30 * Neg Zero + Pos vuz400 * Pos (Succ vuz3100)) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];113 -> 151[label="",style="solid", color="black", weight=3]; 114[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];114 -> 152[label="",style="solid", color="black", weight=3]; 115[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg Zero + Pos vuz400 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];115 -> 153[label="",style="solid", color="black", weight=3]; 116 -> 1539[label="",style="dashed", color="red", weight=0]; 116[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg (Succ vuz3100)) (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg (Succ vuz3100)) (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (primEqInt (Neg (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];116 -> 1540[label="",style="dashed", color="magenta", weight=3]; 116 -> 1541[label="",style="dashed", color="magenta", weight=3]; 116 -> 1542[label="",style="dashed", color="magenta", weight=3]; 116 -> 1543[label="",style="dashed", color="magenta", weight=3]; 116 -> 1544[label="",style="dashed", color="magenta", weight=3]; 116 -> 1545[label="",style="dashed", color="magenta", weight=3]; 116 -> 1546[label="",style="dashed", color="magenta", weight=3]; 117[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Neg (Succ vuz3100)) (Neg Zero) (vuz30 * Pos Zero + Pos vuz400 * Neg (Succ vuz3100)) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];117 -> 156[label="",style="solid", color="black", weight=3]; 118[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];118 -> 157[label="",style="solid", color="black", weight=3]; 119[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos Zero + Pos vuz400 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];119 -> 158[label="",style="solid", color="black", weight=3]; 120 -> 1722[label="",style="dashed", color="red", weight=0]; 120[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg (Succ vuz3100)) (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg (Succ vuz3100)) (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (primEqInt (Pos (primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];120 -> 1723[label="",style="dashed", color="magenta", weight=3]; 120 -> 1724[label="",style="dashed", color="magenta", weight=3]; 120 -> 1725[label="",style="dashed", color="magenta", weight=3]; 120 -> 1726[label="",style="dashed", color="magenta", weight=3]; 120 -> 1727[label="",style="dashed", color="magenta", weight=3]; 120 -> 1728[label="",style="dashed", color="magenta", weight=3]; 120 -> 1729[label="",style="dashed", color="magenta", weight=3]; 121[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Neg (Succ vuz3100)) (Pos Zero) (vuz30 * Neg Zero + Pos vuz400 * Neg (Succ vuz3100)) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];121 -> 161[label="",style="solid", color="black", weight=3]; 122[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];122 -> 162[label="",style="solid", color="black", weight=3]; 123[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg Zero + Pos vuz400 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];123 -> 163[label="",style="solid", color="black", weight=3]; 1964[label="vuz4100",fontsize=16,color="green",shape="box"];1965[label="vuz400",fontsize=16,color="green",shape="box"];1966 -> 1352[label="",style="dashed", color="red", weight=0]; 1966[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1966 -> 2127[label="",style="dashed", color="magenta", weight=3]; 1966 -> 2128[label="",style="dashed", color="magenta", weight=3]; 1967[label="vuz30",fontsize=16,color="green",shape="box"];1968[label="vuz3100",fontsize=16,color="green",shape="box"];1969 -> 1352[label="",style="dashed", color="red", weight=0]; 1969[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1969 -> 2129[label="",style="dashed", color="magenta", weight=3]; 1969 -> 2130[label="",style="dashed", color="magenta", weight=3]; 1970 -> 1352[label="",style="dashed", color="red", weight=0]; 1970[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1970 -> 2131[label="",style="dashed", color="magenta", weight=3]; 1970 -> 2132[label="",style="dashed", color="magenta", weight=3]; 1963[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos vuz145) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6446[label="vuz145/Succ vuz1450",fontsize=10,color="white",style="solid",shape="box"];1963 -> 6446[label="",style="solid", color="burlywood", weight=9]; 6446 -> 2133[label="",style="solid", color="burlywood", weight=3]; 6447[label="vuz145/Zero",fontsize=10,color="white",style="solid",shape="box"];1963 -> 6447[label="",style="solid", color="burlywood", weight=9]; 6447 -> 2134[label="",style="solid", color="burlywood", weight=3]; 126[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Pos (Succ vuz3100)) (Pos Zero) (vuz30 * Pos Zero + Neg vuz400 * Pos (Succ vuz3100)) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];126 -> 166[label="",style="solid", color="black", weight=3]; 127[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];127 -> 167[label="",style="solid", color="black", weight=3]; 128[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos Zero + Neg vuz400 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];128 -> 168[label="",style="solid", color="black", weight=3]; 1031[label="vuz3100",fontsize=16,color="green",shape="box"];1032 -> 1014[label="",style="dashed", color="red", weight=0]; 1032[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1032 -> 1068[label="",style="dashed", color="magenta", weight=3]; 1033[label="vuz30",fontsize=16,color="green",shape="box"];1034 -> 1014[label="",style="dashed", color="red", weight=0]; 1034[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1034 -> 1069[label="",style="dashed", color="magenta", weight=3]; 1035 -> 1014[label="",style="dashed", color="red", weight=0]; 1035[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1035 -> 1070[label="",style="dashed", color="magenta", weight=3]; 1036[label="vuz400",fontsize=16,color="green",shape="box"];1037[label="vuz4100",fontsize=16,color="green",shape="box"];1030[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg vuz69) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6448[label="vuz69/Succ vuz690",fontsize=10,color="white",style="solid",shape="box"];1030 -> 6448[label="",style="solid", color="burlywood", weight=9]; 6448 -> 1071[label="",style="solid", color="burlywood", weight=3]; 6449[label="vuz69/Zero",fontsize=10,color="white",style="solid",shape="box"];1030 -> 6449[label="",style="solid", color="burlywood", weight=9]; 6449 -> 1072[label="",style="solid", color="burlywood", weight=3]; 131[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Pos (Succ vuz3100)) (Neg Zero) (vuz30 * Neg Zero + Neg vuz400 * Pos (Succ vuz3100)) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];131 -> 171[label="",style="solid", color="black", weight=3]; 132[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];132 -> 172[label="",style="solid", color="black", weight=3]; 133[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg Zero + Neg vuz400 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];133 -> 173[label="",style="solid", color="black", weight=3]; 1074[label="vuz4100",fontsize=16,color="green",shape="box"];1075[label="vuz30",fontsize=16,color="green",shape="box"];1076 -> 1014[label="",style="dashed", color="red", weight=0]; 1076[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1076 -> 1111[label="",style="dashed", color="magenta", weight=3]; 1076 -> 1112[label="",style="dashed", color="magenta", weight=3]; 1077[label="vuz3100",fontsize=16,color="green",shape="box"];1078[label="vuz400",fontsize=16,color="green",shape="box"];1079 -> 1014[label="",style="dashed", color="red", weight=0]; 1079[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1079 -> 1113[label="",style="dashed", color="magenta", weight=3]; 1079 -> 1114[label="",style="dashed", color="magenta", weight=3]; 1080 -> 1014[label="",style="dashed", color="red", weight=0]; 1080[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1080 -> 1115[label="",style="dashed", color="magenta", weight=3]; 1080 -> 1116[label="",style="dashed", color="magenta", weight=3]; 1073[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg vuz72) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6450[label="vuz72/Succ vuz720",fontsize=10,color="white",style="solid",shape="box"];1073 -> 6450[label="",style="solid", color="burlywood", weight=9]; 6450 -> 1117[label="",style="solid", color="burlywood", weight=3]; 6451[label="vuz72/Zero",fontsize=10,color="white",style="solid",shape="box"];1073 -> 6451[label="",style="solid", color="burlywood", weight=9]; 6451 -> 1118[label="",style="solid", color="burlywood", weight=3]; 136[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Neg (Succ vuz3100)) (Neg Zero) (vuz30 * Pos Zero + Neg vuz400 * Neg (Succ vuz3100)) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];136 -> 176[label="",style="solid", color="black", weight=3]; 137[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];137 -> 177[label="",style="solid", color="black", weight=3]; 138[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos Zero + Neg vuz400 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];138 -> 178[label="",style="solid", color="black", weight=3]; 1127[label="vuz30",fontsize=16,color="green",shape="box"];1128[label="vuz4100",fontsize=16,color="green",shape="box"];1129[label="vuz400",fontsize=16,color="green",shape="box"];1130 -> 1014[label="",style="dashed", color="red", weight=0]; 1130[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1130 -> 1164[label="",style="dashed", color="magenta", weight=3]; 1131 -> 1014[label="",style="dashed", color="red", weight=0]; 1131[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1131 -> 1165[label="",style="dashed", color="magenta", weight=3]; 1132 -> 1014[label="",style="dashed", color="red", weight=0]; 1132[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1132 -> 1166[label="",style="dashed", color="magenta", weight=3]; 1133[label="vuz3100",fontsize=16,color="green",shape="box"];1126[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos vuz75) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6452[label="vuz75/Succ vuz750",fontsize=10,color="white",style="solid",shape="box"];1126 -> 6452[label="",style="solid", color="burlywood", weight=9]; 6452 -> 1167[label="",style="solid", color="burlywood", weight=3]; 6453[label="vuz75/Zero",fontsize=10,color="white",style="solid",shape="box"];1126 -> 6453[label="",style="solid", color="burlywood", weight=9]; 6453 -> 1168[label="",style="solid", color="burlywood", weight=3]; 141[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Neg (Succ vuz3100)) (Pos Zero) (vuz30 * Neg Zero + Neg vuz400 * Neg (Succ vuz3100)) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];141 -> 181[label="",style="solid", color="black", weight=3]; 142[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];142 -> 182[label="",style="solid", color="black", weight=3]; 143[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg Zero + Neg vuz400 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];143 -> 183[label="",style="solid", color="black", weight=3]; 1187[label="vuz400",fontsize=16,color="green",shape="box"];1188[label="vuz30",fontsize=16,color="green",shape="box"];1189 -> 1014[label="",style="dashed", color="red", weight=0]; 1189[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1189 -> 1337[label="",style="dashed", color="magenta", weight=3]; 1189 -> 1338[label="",style="dashed", color="magenta", weight=3]; 1190 -> 1014[label="",style="dashed", color="red", weight=0]; 1190[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1190 -> 1339[label="",style="dashed", color="magenta", weight=3]; 1190 -> 1340[label="",style="dashed", color="magenta", weight=3]; 1191[label="vuz3100",fontsize=16,color="green",shape="box"];1192[label="vuz4100",fontsize=16,color="green",shape="box"];1193 -> 1014[label="",style="dashed", color="red", weight=0]; 1193[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1193 -> 1341[label="",style="dashed", color="magenta", weight=3]; 1193 -> 1342[label="",style="dashed", color="magenta", weight=3]; 1186[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos vuz78) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6454[label="vuz78/Succ vuz780",fontsize=10,color="white",style="solid",shape="box"];1186 -> 6454[label="",style="solid", color="burlywood", weight=9]; 6454 -> 1343[label="",style="solid", color="burlywood", weight=3]; 6455[label="vuz78/Zero",fontsize=10,color="white",style="solid",shape="box"];1186 -> 6455[label="",style="solid", color="burlywood", weight=9]; 6455 -> 1344[label="",style="solid", color="burlywood", weight=3]; 146[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Pos (Succ vuz3100)) (Pos Zero) (vuz30 * Pos Zero + Pos vuz400 * Pos (Succ vuz3100)) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];146 -> 186[label="",style="solid", color="black", weight=3]; 147[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];147 -> 187[label="",style="solid", color="black", weight=3]; 148[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos Zero + Pos vuz400 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];148 -> 188[label="",style="solid", color="black", weight=3]; 1360[label="vuz30",fontsize=16,color="green",shape="box"];1361[label="vuz4100",fontsize=16,color="green",shape="box"];1362 -> 1014[label="",style="dashed", color="red", weight=0]; 1362[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1362 -> 1517[label="",style="dashed", color="magenta", weight=3]; 1363 -> 1014[label="",style="dashed", color="red", weight=0]; 1363[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1363 -> 1518[label="",style="dashed", color="magenta", weight=3]; 1364[label="vuz400",fontsize=16,color="green",shape="box"];1365 -> 1014[label="",style="dashed", color="red", weight=0]; 1365[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1365 -> 1519[label="",style="dashed", color="magenta", weight=3]; 1366[label="vuz3100",fontsize=16,color="green",shape="box"];1359[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg vuz93) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6456[label="vuz93/Succ vuz930",fontsize=10,color="white",style="solid",shape="box"];1359 -> 6456[label="",style="solid", color="burlywood", weight=9]; 6456 -> 1520[label="",style="solid", color="burlywood", weight=3]; 6457[label="vuz93/Zero",fontsize=10,color="white",style="solid",shape="box"];1359 -> 6457[label="",style="solid", color="burlywood", weight=9]; 6457 -> 1521[label="",style="solid", color="burlywood", weight=3]; 151[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Pos (Succ vuz3100)) (Neg Zero) (vuz30 * Neg Zero + Pos vuz400 * Pos (Succ vuz3100)) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];151 -> 191[label="",style="solid", color="black", weight=3]; 152[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];152 -> 192[label="",style="solid", color="black", weight=3]; 153[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg Zero + Pos vuz400 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];153 -> 193[label="",style="solid", color="black", weight=3]; 1540[label="vuz4100",fontsize=16,color="green",shape="box"];1541 -> 1352[label="",style="dashed", color="red", weight=0]; 1541[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1541 -> 1697[label="",style="dashed", color="magenta", weight=3]; 1541 -> 1698[label="",style="dashed", color="magenta", weight=3]; 1542[label="vuz30",fontsize=16,color="green",shape="box"];1543[label="vuz3100",fontsize=16,color="green",shape="box"];1544 -> 1352[label="",style="dashed", color="red", weight=0]; 1544[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1544 -> 1699[label="",style="dashed", color="magenta", weight=3]; 1544 -> 1700[label="",style="dashed", color="magenta", weight=3]; 1545[label="vuz400",fontsize=16,color="green",shape="box"];1546 -> 1352[label="",style="dashed", color="red", weight=0]; 1546[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1546 -> 1701[label="",style="dashed", color="magenta", weight=3]; 1546 -> 1702[label="",style="dashed", color="magenta", weight=3]; 1539[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg vuz108) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6458[label="vuz108/Succ vuz1080",fontsize=10,color="white",style="solid",shape="box"];1539 -> 6458[label="",style="solid", color="burlywood", weight=9]; 6458 -> 1703[label="",style="solid", color="burlywood", weight=3]; 6459[label="vuz108/Zero",fontsize=10,color="white",style="solid",shape="box"];1539 -> 6459[label="",style="solid", color="burlywood", weight=9]; 6459 -> 1704[label="",style="solid", color="burlywood", weight=3]; 156[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Neg (Succ vuz3100)) (Neg Zero) (vuz30 * Pos Zero + Pos vuz400 * Neg (Succ vuz3100)) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];156 -> 196[label="",style="solid", color="black", weight=3]; 157[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];157 -> 197[label="",style="solid", color="black", weight=3]; 158[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos Zero + Pos vuz400 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];158 -> 198[label="",style="solid", color="black", weight=3]; 1723[label="vuz4100",fontsize=16,color="green",shape="box"];1724[label="vuz400",fontsize=16,color="green",shape="box"];1725 -> 1352[label="",style="dashed", color="red", weight=0]; 1725[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1725 -> 1873[label="",style="dashed", color="magenta", weight=3]; 1725 -> 1874[label="",style="dashed", color="magenta", weight=3]; 1726[label="vuz3100",fontsize=16,color="green",shape="box"];1727 -> 1352[label="",style="dashed", color="red", weight=0]; 1727[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1727 -> 1875[label="",style="dashed", color="magenta", weight=3]; 1727 -> 1876[label="",style="dashed", color="magenta", weight=3]; 1728[label="vuz30",fontsize=16,color="green",shape="box"];1729 -> 1352[label="",style="dashed", color="red", weight=0]; 1729[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];1729 -> 1877[label="",style="dashed", color="magenta", weight=3]; 1729 -> 1878[label="",style="dashed", color="magenta", weight=3]; 1722[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos vuz123) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6460[label="vuz123/Succ vuz1230",fontsize=10,color="white",style="solid",shape="box"];1722 -> 6460[label="",style="solid", color="burlywood", weight=9]; 6460 -> 1879[label="",style="solid", color="burlywood", weight=3]; 6461[label="vuz123/Zero",fontsize=10,color="white",style="solid",shape="box"];1722 -> 6461[label="",style="solid", color="burlywood", weight=9]; 6461 -> 1880[label="",style="solid", color="burlywood", weight=3]; 161[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Neg (Succ vuz3100)) (Pos Zero) (vuz30 * Neg Zero + Pos vuz400 * Neg (Succ vuz3100)) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];161 -> 201[label="",style="solid", color="black", weight=3]; 162[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];162 -> 202[label="",style="solid", color="black", weight=3]; 163[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg Zero + Pos vuz400 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];163 -> 203[label="",style="solid", color="black", weight=3]; 2127[label="Succ vuz4100",fontsize=16,color="green",shape="box"];2128 -> 678[label="",style="dashed", color="red", weight=0]; 2128[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];2128 -> 2147[label="",style="dashed", color="magenta", weight=3]; 2128 -> 2148[label="",style="dashed", color="magenta", weight=3]; 1352[label="primPlusNat vuz660 vuz4100",fontsize=16,color="burlywood",shape="triangle"];6462[label="vuz660/Succ vuz6600",fontsize=10,color="white",style="solid",shape="box"];1352 -> 6462[label="",style="solid", color="burlywood", weight=9]; 6462 -> 1534[label="",style="solid", color="burlywood", weight=3]; 6463[label="vuz660/Zero",fontsize=10,color="white",style="solid",shape="box"];1352 -> 6463[label="",style="solid", color="burlywood", weight=9]; 6463 -> 1535[label="",style="solid", color="burlywood", weight=3]; 2129[label="Succ vuz4100",fontsize=16,color="green",shape="box"];2130 -> 678[label="",style="dashed", color="red", weight=0]; 2130[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];2130 -> 2149[label="",style="dashed", color="magenta", weight=3]; 2130 -> 2150[label="",style="dashed", color="magenta", weight=3]; 2131[label="Succ vuz4100",fontsize=16,color="green",shape="box"];2132 -> 678[label="",style="dashed", color="red", weight=0]; 2132[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];2132 -> 2151[label="",style="dashed", color="magenta", weight=3]; 2132 -> 2152[label="",style="dashed", color="magenta", weight=3]; 2133[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos (Succ vuz1450)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];2133 -> 2153[label="",style="solid", color="black", weight=3]; 2134[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];2134 -> 2154[label="",style="solid", color="black", weight=3]; 166[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Pos (Succ vuz3100)) (Pos Zero) (vuz30 * Pos Zero + Neg vuz400 * Pos (Succ vuz3100)) (Pos Zero) True",fontsize=16,color="black",shape="box"];166 -> 207[label="",style="solid", color="black", weight=3]; 167[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Pos Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];167 -> 208[label="",style="solid", color="black", weight=3]; 168[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos Zero + Neg vuz400 * Pos Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];168 -> 209[label="",style="solid", color="black", weight=3]; 1068 -> 678[label="",style="dashed", color="red", weight=0]; 1068[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1068 -> 1119[label="",style="dashed", color="magenta", weight=3]; 1014[label="primPlusNat vuz66 (Succ vuz4100)",fontsize=16,color="burlywood",shape="triangle"];6464[label="vuz66/Succ vuz660",fontsize=10,color="white",style="solid",shape="box"];1014 -> 6464[label="",style="solid", color="burlywood", weight=9]; 6464 -> 1120[label="",style="solid", color="burlywood", weight=3]; 6465[label="vuz66/Zero",fontsize=10,color="white",style="solid",shape="box"];1014 -> 6465[label="",style="solid", color="burlywood", weight=9]; 6465 -> 1121[label="",style="solid", color="burlywood", weight=3]; 1069 -> 678[label="",style="dashed", color="red", weight=0]; 1069[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1069 -> 1122[label="",style="dashed", color="magenta", weight=3]; 1070 -> 678[label="",style="dashed", color="red", weight=0]; 1070[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1070 -> 1123[label="",style="dashed", color="magenta", weight=3]; 1071[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg (Succ vuz690)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1071 -> 1124[label="",style="solid", color="black", weight=3]; 1072[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1072 -> 1125[label="",style="solid", color="black", weight=3]; 171[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Pos (Succ vuz3100)) (Neg Zero) (vuz30 * Neg Zero + Neg vuz400 * Pos (Succ vuz3100)) (Neg Zero) True",fontsize=16,color="black",shape="box"];171 -> 213[label="",style="solid", color="black", weight=3]; 172[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Pos Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];172 -> 214[label="",style="solid", color="black", weight=3]; 173[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg Zero + Neg vuz400 * Pos Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];173 -> 215[label="",style="solid", color="black", weight=3]; 1111 -> 678[label="",style="dashed", color="red", weight=0]; 1111[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1111 -> 1169[label="",style="dashed", color="magenta", weight=3]; 1111 -> 1170[label="",style="dashed", color="magenta", weight=3]; 1112[label="vuz4100",fontsize=16,color="green",shape="box"];1113 -> 678[label="",style="dashed", color="red", weight=0]; 1113[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1113 -> 1171[label="",style="dashed", color="magenta", weight=3]; 1113 -> 1172[label="",style="dashed", color="magenta", weight=3]; 1114[label="vuz4100",fontsize=16,color="green",shape="box"];1115 -> 678[label="",style="dashed", color="red", weight=0]; 1115[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1115 -> 1173[label="",style="dashed", color="magenta", weight=3]; 1115 -> 1174[label="",style="dashed", color="magenta", weight=3]; 1116[label="vuz4100",fontsize=16,color="green",shape="box"];1117[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg (Succ vuz720)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1117 -> 1175[label="",style="solid", color="black", weight=3]; 1118[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1118 -> 1176[label="",style="solid", color="black", weight=3]; 176[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Neg (Succ vuz3100)) (Neg Zero) (vuz30 * Pos Zero + Neg vuz400 * Neg (Succ vuz3100)) (Neg Zero) True",fontsize=16,color="black",shape="box"];176 -> 219[label="",style="solid", color="black", weight=3]; 177[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos (Succ vuz4100) + Neg vuz400 * Neg Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];177 -> 220[label="",style="solid", color="black", weight=3]; 178[label="reduce2Reduce1 (vuz30 * Pos Zero + Neg vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos Zero + Neg vuz400 * Neg Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];178 -> 221[label="",style="solid", color="black", weight=3]; 1164 -> 678[label="",style="dashed", color="red", weight=0]; 1164[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1164 -> 1345[label="",style="dashed", color="magenta", weight=3]; 1165 -> 678[label="",style="dashed", color="red", weight=0]; 1165[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1165 -> 1346[label="",style="dashed", color="magenta", weight=3]; 1166 -> 678[label="",style="dashed", color="red", weight=0]; 1166[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1166 -> 1347[label="",style="dashed", color="magenta", weight=3]; 1167[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos (Succ vuz750)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1167 -> 1348[label="",style="solid", color="black", weight=3]; 1168[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1168 -> 1349[label="",style="solid", color="black", weight=3]; 181[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Neg (Succ vuz3100)) (Pos Zero) (vuz30 * Neg Zero + Neg vuz400 * Neg (Succ vuz3100)) (Pos Zero) True",fontsize=16,color="black",shape="box"];181 -> 225[label="",style="solid", color="black", weight=3]; 182[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg (Succ vuz4100) + Neg vuz400 * Neg Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];182 -> 226[label="",style="solid", color="black", weight=3]; 183[label="reduce2Reduce1 (vuz30 * Neg Zero + Neg vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg Zero + Neg vuz400 * Neg Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];183 -> 227[label="",style="solid", color="black", weight=3]; 1337 -> 678[label="",style="dashed", color="red", weight=0]; 1337[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1337 -> 1522[label="",style="dashed", color="magenta", weight=3]; 1337 -> 1523[label="",style="dashed", color="magenta", weight=3]; 1338[label="vuz4100",fontsize=16,color="green",shape="box"];1339 -> 678[label="",style="dashed", color="red", weight=0]; 1339[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1339 -> 1524[label="",style="dashed", color="magenta", weight=3]; 1339 -> 1525[label="",style="dashed", color="magenta", weight=3]; 1340[label="vuz4100",fontsize=16,color="green",shape="box"];1341 -> 678[label="",style="dashed", color="red", weight=0]; 1341[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1341 -> 1526[label="",style="dashed", color="magenta", weight=3]; 1341 -> 1527[label="",style="dashed", color="magenta", weight=3]; 1342[label="vuz4100",fontsize=16,color="green",shape="box"];1343[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos (Succ vuz780)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1343 -> 1528[label="",style="solid", color="black", weight=3]; 1344[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1344 -> 1529[label="",style="solid", color="black", weight=3]; 186[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Pos (Succ vuz3100)) (Pos Zero) (vuz30 * Pos Zero + Pos vuz400 * Pos (Succ vuz3100)) (Pos Zero) True",fontsize=16,color="black",shape="box"];186 -> 231[label="",style="solid", color="black", weight=3]; 187[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Pos Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];187 -> 232[label="",style="solid", color="black", weight=3]; 188[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Pos Zero) (Pos Zero) (vuz30 * Pos Zero + Pos vuz400 * Pos Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];188 -> 233[label="",style="solid", color="black", weight=3]; 1517 -> 678[label="",style="dashed", color="red", weight=0]; 1517[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1517 -> 1705[label="",style="dashed", color="magenta", weight=3]; 1518 -> 678[label="",style="dashed", color="red", weight=0]; 1518[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1518 -> 1706[label="",style="dashed", color="magenta", weight=3]; 1519 -> 678[label="",style="dashed", color="red", weight=0]; 1519[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1519 -> 1707[label="",style="dashed", color="magenta", weight=3]; 1520[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg (Succ vuz930)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1520 -> 1708[label="",style="solid", color="black", weight=3]; 1521[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1521 -> 1709[label="",style="solid", color="black", weight=3]; 191[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Pos (Succ vuz3100)) (Neg Zero) (vuz30 * Neg Zero + Pos vuz400 * Pos (Succ vuz3100)) (Neg Zero) True",fontsize=16,color="black",shape="box"];191 -> 237[label="",style="solid", color="black", weight=3]; 192[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Pos Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];192 -> 238[label="",style="solid", color="black", weight=3]; 193[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Pos Zero) (Neg Zero) (vuz30 * Neg Zero + Pos vuz400 * Pos Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];193 -> 239[label="",style="solid", color="black", weight=3]; 1697[label="Succ vuz4100",fontsize=16,color="green",shape="box"];1698 -> 678[label="",style="dashed", color="red", weight=0]; 1698[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1698 -> 1881[label="",style="dashed", color="magenta", weight=3]; 1698 -> 1882[label="",style="dashed", color="magenta", weight=3]; 1699[label="Succ vuz4100",fontsize=16,color="green",shape="box"];1700 -> 678[label="",style="dashed", color="red", weight=0]; 1700[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1700 -> 1883[label="",style="dashed", color="magenta", weight=3]; 1700 -> 1884[label="",style="dashed", color="magenta", weight=3]; 1701[label="Succ vuz4100",fontsize=16,color="green",shape="box"];1702 -> 678[label="",style="dashed", color="red", weight=0]; 1702[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1702 -> 1885[label="",style="dashed", color="magenta", weight=3]; 1702 -> 1886[label="",style="dashed", color="magenta", weight=3]; 1703[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg (Succ vuz1080)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1703 -> 1887[label="",style="solid", color="black", weight=3]; 1704[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1704 -> 1888[label="",style="solid", color="black", weight=3]; 196[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Neg (Succ vuz3100)) (Neg Zero) (vuz30 * Pos Zero + Pos vuz400 * Neg (Succ vuz3100)) (Neg Zero) True",fontsize=16,color="black",shape="box"];196 -> 243[label="",style="solid", color="black", weight=3]; 197[label="reduce2Reduce1 (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos (Succ vuz4100) + Pos vuz400 * Neg Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];197 -> 244[label="",style="solid", color="black", weight=3]; 198[label="reduce2Reduce1 (vuz30 * Pos Zero + Pos vuz400 * Neg Zero) (Neg Zero) (vuz30 * Pos Zero + Pos vuz400 * Neg Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];198 -> 245[label="",style="solid", color="black", weight=3]; 1873[label="Succ vuz4100",fontsize=16,color="green",shape="box"];1874 -> 678[label="",style="dashed", color="red", weight=0]; 1874[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1874 -> 1915[label="",style="dashed", color="magenta", weight=3]; 1875[label="Succ vuz4100",fontsize=16,color="green",shape="box"];1876 -> 678[label="",style="dashed", color="red", weight=0]; 1876[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1876 -> 1916[label="",style="dashed", color="magenta", weight=3]; 1877[label="Succ vuz4100",fontsize=16,color="green",shape="box"];1878 -> 678[label="",style="dashed", color="red", weight=0]; 1878[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];1878 -> 1917[label="",style="dashed", color="magenta", weight=3]; 1879[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos (Succ vuz1230)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1879 -> 1918[label="",style="solid", color="black", weight=3]; 1880[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1880 -> 1919[label="",style="solid", color="black", weight=3]; 201[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Neg (Succ vuz3100)) (Pos Zero) (vuz30 * Neg Zero + Pos vuz400 * Neg (Succ vuz3100)) (Pos Zero) True",fontsize=16,color="black",shape="box"];201 -> 249[label="",style="solid", color="black", weight=3]; 202[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg (Succ vuz4100) + Pos vuz400 * Neg Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];202 -> 250[label="",style="solid", color="black", weight=3]; 203[label="reduce2Reduce1 (vuz30 * Neg Zero + Pos vuz400 * Neg Zero) (Pos Zero) (vuz30 * Neg Zero + Pos vuz400 * Neg Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];203 -> 251[label="",style="solid", color="black", weight=3]; 2147[label="vuz3100",fontsize=16,color="green",shape="box"];2148[label="vuz4100",fontsize=16,color="green",shape="box"];678[label="primMulNat vuz31000 (Succ vuz4100)",fontsize=16,color="burlywood",shape="triangle"];6466[label="vuz31000/Succ vuz310000",fontsize=10,color="white",style="solid",shape="box"];678 -> 6466[label="",style="solid", color="burlywood", weight=9]; 6466 -> 779[label="",style="solid", color="burlywood", weight=3]; 6467[label="vuz31000/Zero",fontsize=10,color="white",style="solid",shape="box"];678 -> 6467[label="",style="solid", color="burlywood", weight=9]; 6467 -> 780[label="",style="solid", color="burlywood", weight=3]; 1534[label="primPlusNat (Succ vuz6600) vuz4100",fontsize=16,color="burlywood",shape="box"];6468[label="vuz4100/Succ vuz41000",fontsize=10,color="white",style="solid",shape="box"];1534 -> 6468[label="",style="solid", color="burlywood", weight=9]; 6468 -> 1715[label="",style="solid", color="burlywood", weight=3]; 6469[label="vuz4100/Zero",fontsize=10,color="white",style="solid",shape="box"];1534 -> 6469[label="",style="solid", color="burlywood", weight=9]; 6469 -> 1716[label="",style="solid", color="burlywood", weight=3]; 1535[label="primPlusNat Zero vuz4100",fontsize=16,color="burlywood",shape="box"];6470[label="vuz4100/Succ vuz41000",fontsize=10,color="white",style="solid",shape="box"];1535 -> 6470[label="",style="solid", color="burlywood", weight=9]; 6470 -> 1717[label="",style="solid", color="burlywood", weight=3]; 6471[label="vuz4100/Zero",fontsize=10,color="white",style="solid",shape="box"];1535 -> 6471[label="",style="solid", color="burlywood", weight=9]; 6471 -> 1718[label="",style="solid", color="burlywood", weight=3]; 2149[label="vuz3100",fontsize=16,color="green",shape="box"];2150[label="vuz4100",fontsize=16,color="green",shape="box"];2151[label="vuz3100",fontsize=16,color="green",shape="box"];2152[label="vuz4100",fontsize=16,color="green",shape="box"];2153[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos (Succ vuz1450)) (Pos Zero))",fontsize=16,color="black",shape="box"];2153 -> 2168[label="",style="solid", color="black", weight=3]; 2154[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];2154 -> 2169[label="",style="solid", color="black", weight=3]; 207[label="error []",fontsize=16,color="black",shape="triangle"];207 -> 255[label="",style="solid", color="black", weight=3]; 208 -> 207[label="",style="dashed", color="red", weight=0]; 208[label="error []",fontsize=16,color="magenta"];209 -> 207[label="",style="dashed", color="red", weight=0]; 209[label="error []",fontsize=16,color="magenta"];1119[label="vuz3100",fontsize=16,color="green",shape="box"];1120[label="primPlusNat (Succ vuz660) (Succ vuz4100)",fontsize=16,color="black",shape="box"];1120 -> 1177[label="",style="solid", color="black", weight=3]; 1121[label="primPlusNat Zero (Succ vuz4100)",fontsize=16,color="black",shape="box"];1121 -> 1178[label="",style="solid", color="black", weight=3]; 1122[label="vuz3100",fontsize=16,color="green",shape="box"];1123[label="vuz3100",fontsize=16,color="green",shape="box"];1124[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg (Succ vuz690)) (Pos Zero))",fontsize=16,color="black",shape="box"];1124 -> 1179[label="",style="solid", color="black", weight=3]; 1125[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1125 -> 1180[label="",style="solid", color="black", weight=3]; 213 -> 207[label="",style="dashed", color="red", weight=0]; 213[label="error []",fontsize=16,color="magenta"];214 -> 207[label="",style="dashed", color="red", weight=0]; 214[label="error []",fontsize=16,color="magenta"];215 -> 207[label="",style="dashed", color="red", weight=0]; 215[label="error []",fontsize=16,color="magenta"];1169[label="vuz3100",fontsize=16,color="green",shape="box"];1170[label="vuz4100",fontsize=16,color="green",shape="box"];1171[label="vuz3100",fontsize=16,color="green",shape="box"];1172[label="vuz4100",fontsize=16,color="green",shape="box"];1173[label="vuz3100",fontsize=16,color="green",shape="box"];1174[label="vuz4100",fontsize=16,color="green",shape="box"];1175[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg (Succ vuz720)) (Pos Zero))",fontsize=16,color="black",shape="box"];1175 -> 1350[label="",style="solid", color="black", weight=3]; 1176[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1176 -> 1351[label="",style="solid", color="black", weight=3]; 219 -> 207[label="",style="dashed", color="red", weight=0]; 219[label="error []",fontsize=16,color="magenta"];220 -> 207[label="",style="dashed", color="red", weight=0]; 220[label="error []",fontsize=16,color="magenta"];221 -> 207[label="",style="dashed", color="red", weight=0]; 221[label="error []",fontsize=16,color="magenta"];1345[label="vuz3100",fontsize=16,color="green",shape="box"];1346[label="vuz3100",fontsize=16,color="green",shape="box"];1347[label="vuz3100",fontsize=16,color="green",shape="box"];1348[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos (Succ vuz750)) (Pos Zero))",fontsize=16,color="black",shape="box"];1348 -> 1530[label="",style="solid", color="black", weight=3]; 1349[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1349 -> 1531[label="",style="solid", color="black", weight=3]; 225 -> 207[label="",style="dashed", color="red", weight=0]; 225[label="error []",fontsize=16,color="magenta"];226 -> 207[label="",style="dashed", color="red", weight=0]; 226[label="error []",fontsize=16,color="magenta"];227 -> 207[label="",style="dashed", color="red", weight=0]; 227[label="error []",fontsize=16,color="magenta"];1522[label="vuz3100",fontsize=16,color="green",shape="box"];1523[label="vuz4100",fontsize=16,color="green",shape="box"];1524[label="vuz3100",fontsize=16,color="green",shape="box"];1525[label="vuz4100",fontsize=16,color="green",shape="box"];1526[label="vuz3100",fontsize=16,color="green",shape="box"];1527[label="vuz4100",fontsize=16,color="green",shape="box"];1528[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos (Succ vuz780)) (Pos Zero))",fontsize=16,color="black",shape="box"];1528 -> 1710[label="",style="solid", color="black", weight=3]; 1529[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1529 -> 1711[label="",style="solid", color="black", weight=3]; 231 -> 207[label="",style="dashed", color="red", weight=0]; 231[label="error []",fontsize=16,color="magenta"];232 -> 207[label="",style="dashed", color="red", weight=0]; 232[label="error []",fontsize=16,color="magenta"];233 -> 207[label="",style="dashed", color="red", weight=0]; 233[label="error []",fontsize=16,color="magenta"];1705[label="vuz3100",fontsize=16,color="green",shape="box"];1706[label="vuz3100",fontsize=16,color="green",shape="box"];1707[label="vuz3100",fontsize=16,color="green",shape="box"];1708[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg (Succ vuz930)) (Pos Zero))",fontsize=16,color="black",shape="box"];1708 -> 1889[label="",style="solid", color="black", weight=3]; 1709[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1709 -> 1890[label="",style="solid", color="black", weight=3]; 237 -> 207[label="",style="dashed", color="red", weight=0]; 237[label="error []",fontsize=16,color="magenta"];238 -> 207[label="",style="dashed", color="red", weight=0]; 238[label="error []",fontsize=16,color="magenta"];239 -> 207[label="",style="dashed", color="red", weight=0]; 239[label="error []",fontsize=16,color="magenta"];1881[label="vuz3100",fontsize=16,color="green",shape="box"];1882[label="vuz4100",fontsize=16,color="green",shape="box"];1883[label="vuz3100",fontsize=16,color="green",shape="box"];1884[label="vuz4100",fontsize=16,color="green",shape="box"];1885[label="vuz3100",fontsize=16,color="green",shape="box"];1886[label="vuz4100",fontsize=16,color="green",shape="box"];1887[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg (Succ vuz1080)) (Pos Zero))",fontsize=16,color="black",shape="box"];1887 -> 1920[label="",style="solid", color="black", weight=3]; 1888[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1888 -> 1921[label="",style="solid", color="black", weight=3]; 243 -> 207[label="",style="dashed", color="red", weight=0]; 243[label="error []",fontsize=16,color="magenta"];244 -> 207[label="",style="dashed", color="red", weight=0]; 244[label="error []",fontsize=16,color="magenta"];245 -> 207[label="",style="dashed", color="red", weight=0]; 245[label="error []",fontsize=16,color="magenta"];1915[label="vuz3100",fontsize=16,color="green",shape="box"];1916[label="vuz3100",fontsize=16,color="green",shape="box"];1917[label="vuz3100",fontsize=16,color="green",shape="box"];1918[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos (Succ vuz1230)) (Pos Zero))",fontsize=16,color="black",shape="box"];1918 -> 1940[label="",style="solid", color="black", weight=3]; 1919[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1919 -> 1941[label="",style="solid", color="black", weight=3]; 249 -> 207[label="",style="dashed", color="red", weight=0]; 249[label="error []",fontsize=16,color="magenta"];250 -> 207[label="",style="dashed", color="red", weight=0]; 250[label="error []",fontsize=16,color="magenta"];251 -> 207[label="",style="dashed", color="red", weight=0]; 251[label="error []",fontsize=16,color="magenta"];779[label="primMulNat (Succ vuz310000) (Succ vuz4100)",fontsize=16,color="black",shape="box"];779 -> 897[label="",style="solid", color="black", weight=3]; 780[label="primMulNat Zero (Succ vuz4100)",fontsize=16,color="black",shape="box"];780 -> 898[label="",style="solid", color="black", weight=3]; 1715[label="primPlusNat (Succ vuz6600) (Succ vuz41000)",fontsize=16,color="black",shape="box"];1715 -> 1893[label="",style="solid", color="black", weight=3]; 1716[label="primPlusNat (Succ vuz6600) Zero",fontsize=16,color="black",shape="box"];1716 -> 1894[label="",style="solid", color="black", weight=3]; 1717[label="primPlusNat Zero (Succ vuz41000)",fontsize=16,color="black",shape="box"];1717 -> 1895[label="",style="solid", color="black", weight=3]; 1718[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];1718 -> 1896[label="",style="solid", color="black", weight=3]; 2168[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) False",fontsize=16,color="black",shape="box"];2168 -> 2185[label="",style="solid", color="black", weight=3]; 2169[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) True",fontsize=16,color="black",shape="box"];2169 -> 2186[label="",style="solid", color="black", weight=3]; 255[label="error []",fontsize=16,color="red",shape="box"];1177[label="Succ (Succ (primPlusNat vuz660 vuz4100))",fontsize=16,color="green",shape="box"];1177 -> 1352[label="",style="dashed", color="green", weight=3]; 1178[label="Succ vuz4100",fontsize=16,color="green",shape="box"];1179[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) False",fontsize=16,color="black",shape="box"];1179 -> 1353[label="",style="solid", color="black", weight=3]; 1180[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) True",fontsize=16,color="black",shape="box"];1180 -> 1354[label="",style="solid", color="black", weight=3]; 1350[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) False",fontsize=16,color="black",shape="box"];1350 -> 1532[label="",style="solid", color="black", weight=3]; 1351[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) True",fontsize=16,color="black",shape="box"];1351 -> 1533[label="",style="solid", color="black", weight=3]; 1530[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) False",fontsize=16,color="black",shape="box"];1530 -> 1712[label="",style="solid", color="black", weight=3]; 1531[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) True",fontsize=16,color="black",shape="box"];1531 -> 1713[label="",style="solid", color="black", weight=3]; 1710[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) False",fontsize=16,color="black",shape="box"];1710 -> 1891[label="",style="solid", color="black", weight=3]; 1711[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) True",fontsize=16,color="black",shape="box"];1711 -> 1892[label="",style="solid", color="black", weight=3]; 1889[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) False",fontsize=16,color="black",shape="box"];1889 -> 1922[label="",style="solid", color="black", weight=3]; 1890[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) True",fontsize=16,color="black",shape="box"];1890 -> 1923[label="",style="solid", color="black", weight=3]; 1920[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) False",fontsize=16,color="black",shape="box"];1920 -> 1942[label="",style="solid", color="black", weight=3]; 1921[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) True",fontsize=16,color="black",shape="box"];1921 -> 1943[label="",style="solid", color="black", weight=3]; 1940[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) False",fontsize=16,color="black",shape="box"];1940 -> 2135[label="",style="solid", color="black", weight=3]; 1941[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) True",fontsize=16,color="black",shape="box"];1941 -> 2136[label="",style="solid", color="black", weight=3]; 897 -> 1014[label="",style="dashed", color="red", weight=0]; 897[label="primPlusNat (primMulNat vuz310000 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];897 -> 1015[label="",style="dashed", color="magenta", weight=3]; 898[label="Zero",fontsize=16,color="green",shape="box"];1893[label="Succ (Succ (primPlusNat vuz6600 vuz41000))",fontsize=16,color="green",shape="box"];1893 -> 1925[label="",style="dashed", color="green", weight=3]; 1894[label="Succ vuz6600",fontsize=16,color="green",shape="box"];1895[label="Succ vuz41000",fontsize=16,color="green",shape="box"];1896[label="Zero",fontsize=16,color="green",shape="box"];2185[label="reduce2Reduce0 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) otherwise",fontsize=16,color="black",shape="box"];2185 -> 2204[label="",style="solid", color="black", weight=3]; 2186 -> 207[label="",style="dashed", color="red", weight=0]; 2186[label="error []",fontsize=16,color="magenta"];1353[label="reduce2Reduce0 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) otherwise",fontsize=16,color="black",shape="box"];1353 -> 1536[label="",style="solid", color="black", weight=3]; 1354 -> 207[label="",style="dashed", color="red", weight=0]; 1354[label="error []",fontsize=16,color="magenta"];1532[label="reduce2Reduce0 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) otherwise",fontsize=16,color="black",shape="box"];1532 -> 1714[label="",style="solid", color="black", weight=3]; 1533 -> 207[label="",style="dashed", color="red", weight=0]; 1533[label="error []",fontsize=16,color="magenta"];1712[label="reduce2Reduce0 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) otherwise",fontsize=16,color="black",shape="box"];1712 -> 1897[label="",style="solid", color="black", weight=3]; 1713 -> 207[label="",style="dashed", color="red", weight=0]; 1713[label="error []",fontsize=16,color="magenta"];1891[label="reduce2Reduce0 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) otherwise",fontsize=16,color="black",shape="box"];1891 -> 1924[label="",style="solid", color="black", weight=3]; 1892 -> 207[label="",style="dashed", color="red", weight=0]; 1892[label="error []",fontsize=16,color="magenta"];1922[label="reduce2Reduce0 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) otherwise",fontsize=16,color="black",shape="box"];1922 -> 1944[label="",style="solid", color="black", weight=3]; 1923 -> 207[label="",style="dashed", color="red", weight=0]; 1923[label="error []",fontsize=16,color="magenta"];1942[label="reduce2Reduce0 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) otherwise",fontsize=16,color="black",shape="box"];1942 -> 2137[label="",style="solid", color="black", weight=3]; 1943 -> 207[label="",style="dashed", color="red", weight=0]; 1943[label="error []",fontsize=16,color="magenta"];2135[label="reduce2Reduce0 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) otherwise",fontsize=16,color="black",shape="box"];2135 -> 2155[label="",style="solid", color="black", weight=3]; 2136 -> 207[label="",style="dashed", color="red", weight=0]; 2136[label="error []",fontsize=16,color="magenta"];1015 -> 678[label="",style="dashed", color="red", weight=0]; 1015[label="primMulNat vuz310000 (Succ vuz4100)",fontsize=16,color="magenta"];1015 -> 1181[label="",style="dashed", color="magenta", weight=3]; 1925 -> 1352[label="",style="dashed", color="red", weight=0]; 1925[label="primPlusNat vuz6600 vuz41000",fontsize=16,color="magenta"];1925 -> 1946[label="",style="dashed", color="magenta", weight=3]; 1925 -> 1947[label="",style="dashed", color="magenta", weight=3]; 2204[label="reduce2Reduce0 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) True",fontsize=16,color="black",shape="box"];2204 -> 2220[label="",style="solid", color="black", weight=3]; 1536[label="reduce2Reduce0 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) True",fontsize=16,color="black",shape="box"];1536 -> 1719[label="",style="solid", color="black", weight=3]; 1714[label="reduce2Reduce0 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) True",fontsize=16,color="black",shape="box"];1714 -> 1898[label="",style="solid", color="black", weight=3]; 1897[label="reduce2Reduce0 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) True",fontsize=16,color="black",shape="box"];1897 -> 1926[label="",style="solid", color="black", weight=3]; 1924[label="reduce2Reduce0 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) True",fontsize=16,color="black",shape="box"];1924 -> 1945[label="",style="solid", color="black", weight=3]; 1944[label="reduce2Reduce0 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) True",fontsize=16,color="black",shape="box"];1944 -> 2138[label="",style="solid", color="black", weight=3]; 2137[label="reduce2Reduce0 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) True",fontsize=16,color="black",shape="box"];2137 -> 2156[label="",style="solid", color="black", weight=3]; 2155[label="reduce2Reduce0 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) True",fontsize=16,color="black",shape="box"];2155 -> 2170[label="",style="solid", color="black", weight=3]; 1181[label="vuz310000",fontsize=16,color="green",shape="box"];1946[label="vuz41000",fontsize=16,color="green",shape="box"];1947[label="vuz6600",fontsize=16,color="green",shape="box"];2220[label="(vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) `quot` reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) :% (Pos vuz143 `quot` reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144))",fontsize=16,color="green",shape="box"];2220 -> 2235[label="",style="dashed", color="green", weight=3]; 2220 -> 2236[label="",style="dashed", color="green", weight=3]; 1719[label="(vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) `quot` reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) :% (Neg vuz67 `quot` reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68))",fontsize=16,color="green",shape="box"];1719 -> 1899[label="",style="dashed", color="green", weight=3]; 1719 -> 1900[label="",style="dashed", color="green", weight=3]; 1898[label="(vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) `quot` reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) :% (Neg vuz70 `quot` reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71))",fontsize=16,color="green",shape="box"];1898 -> 1927[label="",style="dashed", color="green", weight=3]; 1898 -> 1928[label="",style="dashed", color="green", weight=3]; 1926[label="(vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) `quot` reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) :% (Pos vuz73 `quot` reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74))",fontsize=16,color="green",shape="box"];1926 -> 1948[label="",style="dashed", color="green", weight=3]; 1926 -> 1949[label="",style="dashed", color="green", weight=3]; 1945[label="(vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) `quot` reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) :% (Pos vuz76 `quot` reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77))",fontsize=16,color="green",shape="box"];1945 -> 2139[label="",style="dashed", color="green", weight=3]; 1945 -> 2140[label="",style="dashed", color="green", weight=3]; 2138[label="(vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) `quot` reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) :% (Neg vuz91 `quot` reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92))",fontsize=16,color="green",shape="box"];2138 -> 2157[label="",style="dashed", color="green", weight=3]; 2138 -> 2158[label="",style="dashed", color="green", weight=3]; 2156[label="(vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) `quot` reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) :% (Neg vuz106 `quot` reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107))",fontsize=16,color="green",shape="box"];2156 -> 2171[label="",style="dashed", color="green", weight=3]; 2156 -> 2172[label="",style="dashed", color="green", weight=3]; 2170[label="(vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) `quot` reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) :% (Pos vuz121 `quot` reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122))",fontsize=16,color="green",shape="box"];2170 -> 2187[label="",style="dashed", color="green", weight=3]; 2170 -> 2188[label="",style="dashed", color="green", weight=3]; 2235[label="(vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) `quot` reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];2235 -> 2248[label="",style="solid", color="black", weight=3]; 2236[label="Pos vuz143 `quot` reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];2236 -> 2249[label="",style="solid", color="black", weight=3]; 1899[label="(vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) `quot` reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];1899 -> 1929[label="",style="solid", color="black", weight=3]; 1900[label="Neg vuz67 `quot` reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];1900 -> 1930[label="",style="solid", color="black", weight=3]; 1927[label="(vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) `quot` reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];1927 -> 1950[label="",style="solid", color="black", weight=3]; 1928[label="Neg vuz70 `quot` reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];1928 -> 1951[label="",style="solid", color="black", weight=3]; 1948[label="(vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) `quot` reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];1948 -> 2141[label="",style="solid", color="black", weight=3]; 1949[label="Pos vuz73 `quot` reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];1949 -> 2142[label="",style="solid", color="black", weight=3]; 2139[label="(vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) `quot` reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];2139 -> 2159[label="",style="solid", color="black", weight=3]; 2140[label="Pos vuz76 `quot` reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];2140 -> 2160[label="",style="solid", color="black", weight=3]; 2157[label="(vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) `quot` reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];2157 -> 2173[label="",style="solid", color="black", weight=3]; 2158[label="Neg vuz91 `quot` reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];2158 -> 2174[label="",style="solid", color="black", weight=3]; 2171[label="(vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) `quot` reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];2171 -> 2189[label="",style="solid", color="black", weight=3]; 2172[label="Neg vuz106 `quot` reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];2172 -> 2190[label="",style="solid", color="black", weight=3]; 2187[label="(vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) `quot` reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];2187 -> 2205[label="",style="solid", color="black", weight=3]; 2188[label="Pos vuz121 `quot` reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];2188 -> 2206[label="",style="solid", color="black", weight=3]; 2248[label="primQuotInt (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144))",fontsize=16,color="black",shape="box"];2248 -> 2260[label="",style="solid", color="black", weight=3]; 2249 -> 5044[label="",style="dashed", color="red", weight=0]; 2249[label="primQuotInt (Pos vuz143) (reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144))",fontsize=16,color="magenta"];2249 -> 5045[label="",style="dashed", color="magenta", weight=3]; 2249 -> 5046[label="",style="dashed", color="magenta", weight=3]; 1929[label="primQuotInt (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68))",fontsize=16,color="black",shape="box"];1929 -> 1958[label="",style="solid", color="black", weight=3]; 1930 -> 3507[label="",style="dashed", color="red", weight=0]; 1930[label="primQuotInt (Neg vuz67) (reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68))",fontsize=16,color="magenta"];1930 -> 3508[label="",style="dashed", color="magenta", weight=3]; 1930 -> 3509[label="",style="dashed", color="magenta", weight=3]; 1950[label="primQuotInt (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71))",fontsize=16,color="black",shape="box"];1950 -> 2143[label="",style="solid", color="black", weight=3]; 1951 -> 3507[label="",style="dashed", color="red", weight=0]; 1951[label="primQuotInt (Neg vuz70) (reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71))",fontsize=16,color="magenta"];1951 -> 3510[label="",style="dashed", color="magenta", weight=3]; 1951 -> 3511[label="",style="dashed", color="magenta", weight=3]; 2141[label="primQuotInt (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74))",fontsize=16,color="black",shape="box"];2141 -> 2161[label="",style="solid", color="black", weight=3]; 2142 -> 5044[label="",style="dashed", color="red", weight=0]; 2142[label="primQuotInt (Pos vuz73) (reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74))",fontsize=16,color="magenta"];2142 -> 5047[label="",style="dashed", color="magenta", weight=3]; 2159[label="primQuotInt (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77))",fontsize=16,color="black",shape="box"];2159 -> 2175[label="",style="solid", color="black", weight=3]; 2160 -> 5044[label="",style="dashed", color="red", weight=0]; 2160[label="primQuotInt (Pos vuz76) (reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77))",fontsize=16,color="magenta"];2160 -> 5048[label="",style="dashed", color="magenta", weight=3]; 2160 -> 5049[label="",style="dashed", color="magenta", weight=3]; 2173[label="primQuotInt (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92))",fontsize=16,color="black",shape="box"];2173 -> 2191[label="",style="solid", color="black", weight=3]; 2174 -> 3507[label="",style="dashed", color="red", weight=0]; 2174[label="primQuotInt (Neg vuz91) (reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92))",fontsize=16,color="magenta"];2174 -> 3512[label="",style="dashed", color="magenta", weight=3]; 2174 -> 3513[label="",style="dashed", color="magenta", weight=3]; 2189[label="primQuotInt (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107))",fontsize=16,color="black",shape="box"];2189 -> 2207[label="",style="solid", color="black", weight=3]; 2190 -> 3507[label="",style="dashed", color="red", weight=0]; 2190[label="primQuotInt (Neg vuz106) (reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107))",fontsize=16,color="magenta"];2190 -> 3514[label="",style="dashed", color="magenta", weight=3]; 2190 -> 3515[label="",style="dashed", color="magenta", weight=3]; 2205[label="primQuotInt (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122))",fontsize=16,color="black",shape="box"];2205 -> 2221[label="",style="solid", color="black", weight=3]; 2206 -> 5044[label="",style="dashed", color="red", weight=0]; 2206[label="primQuotInt (Pos vuz121) (reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122))",fontsize=16,color="magenta"];2206 -> 5050[label="",style="dashed", color="magenta", weight=3]; 2206 -> 5051[label="",style="dashed", color="magenta", weight=3]; 2260[label="primQuotInt (primPlusInt (vuz9 * Pos (Succ vuz10)) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (vuz9 * Pos (Succ vuz10)) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2260 -> 2268[label="",style="solid", color="black", weight=3]; 5045[label="vuz143",fontsize=16,color="green",shape="box"];5046[label="reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5046 -> 5681[label="",style="solid", color="black", weight=3]; 5044[label="primQuotInt (Pos vuz73) vuz346",fontsize=16,color="burlywood",shape="triangle"];6472[label="vuz346/Pos vuz3460",fontsize=10,color="white",style="solid",shape="box"];5044 -> 6472[label="",style="solid", color="burlywood", weight=9]; 6472 -> 5682[label="",style="solid", color="burlywood", weight=3]; 6473[label="vuz346/Neg vuz3460",fontsize=10,color="white",style="solid",shape="box"];5044 -> 6473[label="",style="solid", color="burlywood", weight=9]; 6473 -> 5683[label="",style="solid", color="burlywood", weight=3]; 1958[label="primQuotInt (primPlusInt (vuz20 * Neg (Succ vuz21)) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (vuz20 * Neg (Succ vuz21)) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="box"];1958 -> 2145[label="",style="solid", color="black", weight=3]; 3508[label="reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];3508 -> 4082[label="",style="solid", color="black", weight=3]; 3509[label="vuz67",fontsize=16,color="green",shape="box"];3507[label="primQuotInt (Neg vuz280) vuz281",fontsize=16,color="burlywood",shape="triangle"];6474[label="vuz281/Pos vuz2810",fontsize=10,color="white",style="solid",shape="box"];3507 -> 6474[label="",style="solid", color="burlywood", weight=9]; 6474 -> 4083[label="",style="solid", color="burlywood", weight=3]; 6475[label="vuz281/Neg vuz2810",fontsize=10,color="white",style="solid",shape="box"];3507 -> 6475[label="",style="solid", color="burlywood", weight=9]; 6475 -> 4084[label="",style="solid", color="burlywood", weight=3]; 2143[label="primQuotInt (primPlusInt (vuz25 * Pos (Succ vuz26)) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (vuz25 * Pos (Succ vuz26)) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2143 -> 2163[label="",style="solid", color="black", weight=3]; 3510[label="reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];3510 -> 4085[label="",style="solid", color="black", weight=3]; 3511[label="vuz70",fontsize=16,color="green",shape="box"];2161[label="primQuotInt (primPlusInt (vuz30 * Neg (Succ vuz31)) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (vuz30 * Neg (Succ vuz31)) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2161 -> 2177[label="",style="solid", color="black", weight=3]; 5047[label="reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5047 -> 5684[label="",style="solid", color="black", weight=3]; 2175[label="primQuotInt (primPlusInt (vuz35 * Pos (Succ vuz36)) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (vuz35 * Pos (Succ vuz36)) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2175 -> 2193[label="",style="solid", color="black", weight=3]; 5048[label="vuz76",fontsize=16,color="green",shape="box"];5049[label="reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5049 -> 5685[label="",style="solid", color="black", weight=3]; 2191[label="primQuotInt (primPlusInt (vuz40 * Neg (Succ vuz41)) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (vuz40 * Neg (Succ vuz41)) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2191 -> 2209[label="",style="solid", color="black", weight=3]; 3512[label="reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];3512 -> 4086[label="",style="solid", color="black", weight=3]; 3513[label="vuz91",fontsize=16,color="green",shape="box"];2207[label="primQuotInt (primPlusInt (vuz45 * Pos (Succ vuz46)) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (vuz45 * Pos (Succ vuz46)) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2207 -> 2223[label="",style="solid", color="black", weight=3]; 3514[label="reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];3514 -> 4087[label="",style="solid", color="black", weight=3]; 3515[label="vuz106",fontsize=16,color="green",shape="box"];2221[label="primQuotInt (primPlusInt (vuz50 * Neg (Succ vuz51)) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (vuz50 * Neg (Succ vuz51)) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2221 -> 2237[label="",style="solid", color="black", weight=3]; 5050[label="vuz121",fontsize=16,color="green",shape="box"];5051[label="reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5051 -> 5686[label="",style="solid", color="black", weight=3]; 2268[label="primQuotInt (primPlusInt (primMulInt vuz9 (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (primMulInt vuz9 (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="burlywood",shape="box"];6476[label="vuz9/Pos vuz90",fontsize=10,color="white",style="solid",shape="box"];2268 -> 6476[label="",style="solid", color="burlywood", weight=9]; 6476 -> 2274[label="",style="solid", color="burlywood", weight=3]; 6477[label="vuz9/Neg vuz90",fontsize=10,color="white",style="solid",shape="box"];2268 -> 6477[label="",style="solid", color="burlywood", weight=9]; 6477 -> 2275[label="",style="solid", color="burlywood", weight=3]; 5681[label="gcd (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5681 -> 5695[label="",style="solid", color="black", weight=3]; 5682[label="primQuotInt (Pos vuz73) (Pos vuz3460)",fontsize=16,color="burlywood",shape="box"];6478[label="vuz3460/Succ vuz34600",fontsize=10,color="white",style="solid",shape="box"];5682 -> 6478[label="",style="solid", color="burlywood", weight=9]; 6478 -> 5696[label="",style="solid", color="burlywood", weight=3]; 6479[label="vuz3460/Zero",fontsize=10,color="white",style="solid",shape="box"];5682 -> 6479[label="",style="solid", color="burlywood", weight=9]; 6479 -> 5697[label="",style="solid", color="burlywood", weight=3]; 5683[label="primQuotInt (Pos vuz73) (Neg vuz3460)",fontsize=16,color="burlywood",shape="box"];6480[label="vuz3460/Succ vuz34600",fontsize=10,color="white",style="solid",shape="box"];5683 -> 6480[label="",style="solid", color="burlywood", weight=9]; 6480 -> 5698[label="",style="solid", color="burlywood", weight=3]; 6481[label="vuz3460/Zero",fontsize=10,color="white",style="solid",shape="box"];5683 -> 6481[label="",style="solid", color="burlywood", weight=9]; 6481 -> 5699[label="",style="solid", color="burlywood", weight=3]; 2145[label="primQuotInt (primPlusInt (primMulInt vuz20 (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (primMulInt vuz20 (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="burlywood",shape="box"];6482[label="vuz20/Pos vuz200",fontsize=10,color="white",style="solid",shape="box"];2145 -> 6482[label="",style="solid", color="burlywood", weight=9]; 6482 -> 2165[label="",style="solid", color="burlywood", weight=3]; 6483[label="vuz20/Neg vuz200",fontsize=10,color="white",style="solid",shape="box"];2145 -> 6483[label="",style="solid", color="burlywood", weight=9]; 6483 -> 2166[label="",style="solid", color="burlywood", weight=3]; 4082[label="gcd (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4082 -> 4091[label="",style="solid", color="black", weight=3]; 4083[label="primQuotInt (Neg vuz280) (Pos vuz2810)",fontsize=16,color="burlywood",shape="box"];6484[label="vuz2810/Succ vuz28100",fontsize=10,color="white",style="solid",shape="box"];4083 -> 6484[label="",style="solid", color="burlywood", weight=9]; 6484 -> 4092[label="",style="solid", color="burlywood", weight=3]; 6485[label="vuz2810/Zero",fontsize=10,color="white",style="solid",shape="box"];4083 -> 6485[label="",style="solid", color="burlywood", weight=9]; 6485 -> 4093[label="",style="solid", color="burlywood", weight=3]; 4084[label="primQuotInt (Neg vuz280) (Neg vuz2810)",fontsize=16,color="burlywood",shape="box"];6486[label="vuz2810/Succ vuz28100",fontsize=10,color="white",style="solid",shape="box"];4084 -> 6486[label="",style="solid", color="burlywood", weight=9]; 6486 -> 4094[label="",style="solid", color="burlywood", weight=3]; 6487[label="vuz2810/Zero",fontsize=10,color="white",style="solid",shape="box"];4084 -> 6487[label="",style="solid", color="burlywood", weight=9]; 6487 -> 4095[label="",style="solid", color="burlywood", weight=3]; 2163[label="primQuotInt (primPlusInt (primMulInt vuz25 (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (primMulInt vuz25 (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="burlywood",shape="box"];6488[label="vuz25/Pos vuz250",fontsize=10,color="white",style="solid",shape="box"];2163 -> 6488[label="",style="solid", color="burlywood", weight=9]; 6488 -> 2179[label="",style="solid", color="burlywood", weight=3]; 6489[label="vuz25/Neg vuz250",fontsize=10,color="white",style="solid",shape="box"];2163 -> 6489[label="",style="solid", color="burlywood", weight=9]; 6489 -> 2180[label="",style="solid", color="burlywood", weight=3]; 4085[label="gcd (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];4085 -> 4096[label="",style="solid", color="black", weight=3]; 2177[label="primQuotInt (primPlusInt (primMulInt vuz30 (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (primMulInt vuz30 (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="burlywood",shape="box"];6490[label="vuz30/Pos vuz300",fontsize=10,color="white",style="solid",shape="box"];2177 -> 6490[label="",style="solid", color="burlywood", weight=9]; 6490 -> 2195[label="",style="solid", color="burlywood", weight=3]; 6491[label="vuz30/Neg vuz300",fontsize=10,color="white",style="solid",shape="box"];2177 -> 6491[label="",style="solid", color="burlywood", weight=9]; 6491 -> 2196[label="",style="solid", color="burlywood", weight=3]; 5684[label="gcd (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5684 -> 5700[label="",style="solid", color="black", weight=3]; 2193[label="primQuotInt (primPlusInt (primMulInt vuz35 (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (primMulInt vuz35 (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="burlywood",shape="box"];6492[label="vuz35/Pos vuz350",fontsize=10,color="white",style="solid",shape="box"];2193 -> 6492[label="",style="solid", color="burlywood", weight=9]; 6492 -> 2211[label="",style="solid", color="burlywood", weight=3]; 6493[label="vuz35/Neg vuz350",fontsize=10,color="white",style="solid",shape="box"];2193 -> 6493[label="",style="solid", color="burlywood", weight=9]; 6493 -> 2212[label="",style="solid", color="burlywood", weight=3]; 5685[label="gcd (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5685 -> 5701[label="",style="solid", color="black", weight=3]; 2209[label="primQuotInt (primPlusInt (primMulInt vuz40 (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (primMulInt vuz40 (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="burlywood",shape="box"];6494[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];2209 -> 6494[label="",style="solid", color="burlywood", weight=9]; 6494 -> 2225[label="",style="solid", color="burlywood", weight=3]; 6495[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];2209 -> 6495[label="",style="solid", color="burlywood", weight=9]; 6495 -> 2226[label="",style="solid", color="burlywood", weight=3]; 4086[label="gcd (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];4086 -> 4097[label="",style="solid", color="black", weight=3]; 2223[label="primQuotInt (primPlusInt (primMulInt vuz45 (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (primMulInt vuz45 (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="burlywood",shape="box"];6496[label="vuz45/Pos vuz450",fontsize=10,color="white",style="solid",shape="box"];2223 -> 6496[label="",style="solid", color="burlywood", weight=9]; 6496 -> 2239[label="",style="solid", color="burlywood", weight=3]; 6497[label="vuz45/Neg vuz450",fontsize=10,color="white",style="solid",shape="box"];2223 -> 6497[label="",style="solid", color="burlywood", weight=9]; 6497 -> 2240[label="",style="solid", color="burlywood", weight=3]; 4087[label="gcd (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];4087 -> 4098[label="",style="solid", color="black", weight=3]; 2237[label="primQuotInt (primPlusInt (primMulInt vuz50 (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (primMulInt vuz50 (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="burlywood",shape="box"];6498[label="vuz50/Pos vuz500",fontsize=10,color="white",style="solid",shape="box"];2237 -> 6498[label="",style="solid", color="burlywood", weight=9]; 6498 -> 2250[label="",style="solid", color="burlywood", weight=3]; 6499[label="vuz50/Neg vuz500",fontsize=10,color="white",style="solid",shape="box"];2237 -> 6499[label="",style="solid", color="burlywood", weight=9]; 6499 -> 2251[label="",style="solid", color="burlywood", weight=3]; 5686[label="gcd (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5686 -> 5702[label="",style="solid", color="black", weight=3]; 2274[label="primQuotInt (primPlusInt (primMulInt (Pos vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (primMulInt (Pos vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2274 -> 2280[label="",style="solid", color="black", weight=3]; 2275[label="primQuotInt (primPlusInt (primMulInt (Neg vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (primMulInt (Neg vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2275 -> 2281[label="",style="solid", color="black", weight=3]; 5695[label="gcd3 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5695 -> 5711[label="",style="solid", color="black", weight=3]; 5696[label="primQuotInt (Pos vuz73) (Pos (Succ vuz34600))",fontsize=16,color="black",shape="box"];5696 -> 5712[label="",style="solid", color="black", weight=3]; 5697[label="primQuotInt (Pos vuz73) (Pos Zero)",fontsize=16,color="black",shape="box"];5697 -> 5713[label="",style="solid", color="black", weight=3]; 5698[label="primQuotInt (Pos vuz73) (Neg (Succ vuz34600))",fontsize=16,color="black",shape="box"];5698 -> 5714[label="",style="solid", color="black", weight=3]; 5699[label="primQuotInt (Pos vuz73) (Neg Zero)",fontsize=16,color="black",shape="box"];5699 -> 5715[label="",style="solid", color="black", weight=3]; 2165[label="primQuotInt (primPlusInt (primMulInt (Pos vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (primMulInt (Pos vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="box"];2165 -> 2182[label="",style="solid", color="black", weight=3]; 2166[label="primQuotInt (primPlusInt (primMulInt (Neg vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (primMulInt (Neg vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="box"];2166 -> 2183[label="",style="solid", color="black", weight=3]; 4091[label="gcd3 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4091 -> 4104[label="",style="solid", color="black", weight=3]; 4092[label="primQuotInt (Neg vuz280) (Pos (Succ vuz28100))",fontsize=16,color="black",shape="box"];4092 -> 4105[label="",style="solid", color="black", weight=3]; 4093[label="primQuotInt (Neg vuz280) (Pos Zero)",fontsize=16,color="black",shape="box"];4093 -> 4106[label="",style="solid", color="black", weight=3]; 4094[label="primQuotInt (Neg vuz280) (Neg (Succ vuz28100))",fontsize=16,color="black",shape="box"];4094 -> 4107[label="",style="solid", color="black", weight=3]; 4095[label="primQuotInt (Neg vuz280) (Neg Zero)",fontsize=16,color="black",shape="box"];4095 -> 4108[label="",style="solid", color="black", weight=3]; 2179[label="primQuotInt (primPlusInt (primMulInt (Pos vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (primMulInt (Pos vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2179 -> 2198[label="",style="solid", color="black", weight=3]; 2180[label="primQuotInt (primPlusInt (primMulInt (Neg vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (primMulInt (Neg vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2180 -> 2199[label="",style="solid", color="black", weight=3]; 4096[label="gcd3 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];4096 -> 4109[label="",style="solid", color="black", weight=3]; 2195[label="primQuotInt (primPlusInt (primMulInt (Pos vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (primMulInt (Pos vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2195 -> 2214[label="",style="solid", color="black", weight=3]; 2196[label="primQuotInt (primPlusInt (primMulInt (Neg vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (primMulInt (Neg vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2196 -> 2215[label="",style="solid", color="black", weight=3]; 5700[label="gcd3 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5700 -> 5716[label="",style="solid", color="black", weight=3]; 2211[label="primQuotInt (primPlusInt (primMulInt (Pos vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (primMulInt (Pos vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2211 -> 2228[label="",style="solid", color="black", weight=3]; 2212[label="primQuotInt (primPlusInt (primMulInt (Neg vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (primMulInt (Neg vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2212 -> 2229[label="",style="solid", color="black", weight=3]; 5701[label="gcd3 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5701 -> 5717[label="",style="solid", color="black", weight=3]; 2225[label="primQuotInt (primPlusInt (primMulInt (Pos vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (primMulInt (Pos vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2225 -> 2242[label="",style="solid", color="black", weight=3]; 2226[label="primQuotInt (primPlusInt (primMulInt (Neg vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (primMulInt (Neg vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2226 -> 2243[label="",style="solid", color="black", weight=3]; 4097[label="gcd3 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];4097 -> 4110[label="",style="solid", color="black", weight=3]; 2239[label="primQuotInt (primPlusInt (primMulInt (Pos vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (primMulInt (Pos vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2239 -> 2253[label="",style="solid", color="black", weight=3]; 2240[label="primQuotInt (primPlusInt (primMulInt (Neg vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (primMulInt (Neg vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2240 -> 2254[label="",style="solid", color="black", weight=3]; 4098[label="gcd3 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];4098 -> 4111[label="",style="solid", color="black", weight=3]; 2250[label="primQuotInt (primPlusInt (primMulInt (Pos vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (primMulInt (Pos vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2250 -> 2262[label="",style="solid", color="black", weight=3]; 2251[label="primQuotInt (primPlusInt (primMulInt (Neg vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (primMulInt (Neg vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2251 -> 2263[label="",style="solid", color="black", weight=3]; 5702[label="gcd3 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5702 -> 5718[label="",style="solid", color="black", weight=3]; 2280 -> 2287[label="",style="dashed", color="red", weight=0]; 2280[label="primQuotInt (primPlusInt (Pos (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (Pos (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="magenta"];2280 -> 2288[label="",style="dashed", color="magenta", weight=3]; 2280 -> 2289[label="",style="dashed", color="magenta", weight=3]; 2281 -> 2290[label="",style="dashed", color="red", weight=0]; 2281[label="primQuotInt (primPlusInt (Neg (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (Neg (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="magenta"];2281 -> 2291[label="",style="dashed", color="magenta", weight=3]; 2281 -> 2292[label="",style="dashed", color="magenta", weight=3]; 5711[label="gcd2 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12) == fromInt (Pos Zero)) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5711 -> 5733[label="",style="solid", color="black", weight=3]; 5712[label="Pos (primDivNatS vuz73 (Succ vuz34600))",fontsize=16,color="green",shape="box"];5712 -> 5734[label="",style="dashed", color="green", weight=3]; 5713 -> 4106[label="",style="dashed", color="red", weight=0]; 5713[label="error []",fontsize=16,color="magenta"];5714[label="Neg (primDivNatS vuz73 (Succ vuz34600))",fontsize=16,color="green",shape="box"];5714 -> 5735[label="",style="dashed", color="green", weight=3]; 5715 -> 4106[label="",style="dashed", color="red", weight=0]; 5715[label="error []",fontsize=16,color="magenta"];2182 -> 2201[label="",style="dashed", color="red", weight=0]; 2182[label="primQuotInt (primPlusInt (Neg (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (Neg (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="magenta"];2182 -> 2202[label="",style="dashed", color="magenta", weight=3]; 2182 -> 2203[label="",style="dashed", color="magenta", weight=3]; 2183 -> 2217[label="",style="dashed", color="red", weight=0]; 2183[label="primQuotInt (primPlusInt (Pos (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (Pos (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="magenta"];2183 -> 2218[label="",style="dashed", color="magenta", weight=3]; 2183 -> 2219[label="",style="dashed", color="magenta", weight=3]; 4104[label="gcd2 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23) == fromInt (Pos Zero)) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4104 -> 4126[label="",style="solid", color="black", weight=3]; 4105[label="Neg (primDivNatS vuz280 (Succ vuz28100))",fontsize=16,color="green",shape="box"];4105 -> 4127[label="",style="dashed", color="green", weight=3]; 4106[label="error []",fontsize=16,color="black",shape="triangle"];4106 -> 4128[label="",style="solid", color="black", weight=3]; 4107[label="Pos (primDivNatS vuz280 (Succ vuz28100))",fontsize=16,color="green",shape="box"];4107 -> 4129[label="",style="dashed", color="green", weight=3]; 4108 -> 4106[label="",style="dashed", color="red", weight=0]; 4108[label="error []",fontsize=16,color="magenta"];2198 -> 2232[label="",style="dashed", color="red", weight=0]; 2198[label="primQuotInt (primPlusInt (Pos (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (Pos (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="magenta"];2198 -> 2233[label="",style="dashed", color="magenta", weight=3]; 2198 -> 2234[label="",style="dashed", color="magenta", weight=3]; 2199 -> 2245[label="",style="dashed", color="red", weight=0]; 2199[label="primQuotInt (primPlusInt (Neg (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (Neg (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="magenta"];2199 -> 2246[label="",style="dashed", color="magenta", weight=3]; 2199 -> 2247[label="",style="dashed", color="magenta", weight=3]; 4109[label="gcd2 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28) == fromInt (Pos Zero)) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];4109 -> 4130[label="",style="solid", color="black", weight=3]; 2214 -> 2257[label="",style="dashed", color="red", weight=0]; 2214[label="primQuotInt (primPlusInt (Neg (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (Neg (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="magenta"];2214 -> 2258[label="",style="dashed", color="magenta", weight=3]; 2214 -> 2259[label="",style="dashed", color="magenta", weight=3]; 2215 -> 2265[label="",style="dashed", color="red", weight=0]; 2215[label="primQuotInt (primPlusInt (Pos (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (Pos (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="magenta"];2215 -> 2266[label="",style="dashed", color="magenta", weight=3]; 2215 -> 2267[label="",style="dashed", color="magenta", weight=3]; 5716[label="gcd2 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33) == fromInt (Pos Zero)) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5716 -> 5736[label="",style="solid", color="black", weight=3]; 2228 -> 2271[label="",style="dashed", color="red", weight=0]; 2228[label="primQuotInt (primPlusInt (Pos (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (Pos (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="magenta"];2228 -> 2272[label="",style="dashed", color="magenta", weight=3]; 2228 -> 2273[label="",style="dashed", color="magenta", weight=3]; 2229 -> 2277[label="",style="dashed", color="red", weight=0]; 2229[label="primQuotInt (primPlusInt (Neg (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (Neg (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="magenta"];2229 -> 2278[label="",style="dashed", color="magenta", weight=3]; 2229 -> 2279[label="",style="dashed", color="magenta", weight=3]; 5717[label="gcd2 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38) == fromInt (Pos Zero)) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5717 -> 5737[label="",style="solid", color="black", weight=3]; 2242 -> 2284[label="",style="dashed", color="red", weight=0]; 2242[label="primQuotInt (primPlusInt (Neg (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (Neg (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="magenta"];2242 -> 2285[label="",style="dashed", color="magenta", weight=3]; 2242 -> 2286[label="",style="dashed", color="magenta", weight=3]; 2243 -> 2294[label="",style="dashed", color="red", weight=0]; 2243[label="primQuotInt (primPlusInt (Pos (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (Pos (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="magenta"];2243 -> 2295[label="",style="dashed", color="magenta", weight=3]; 2243 -> 2296[label="",style="dashed", color="magenta", weight=3]; 4110[label="gcd2 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43) == fromInt (Pos Zero)) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];4110 -> 4131[label="",style="solid", color="black", weight=3]; 2253 -> 2298[label="",style="dashed", color="red", weight=0]; 2253[label="primQuotInt (primPlusInt (Pos (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (Pos (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="magenta"];2253 -> 2299[label="",style="dashed", color="magenta", weight=3]; 2253 -> 2300[label="",style="dashed", color="magenta", weight=3]; 2254 -> 2301[label="",style="dashed", color="red", weight=0]; 2254[label="primQuotInt (primPlusInt (Neg (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (Neg (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="magenta"];2254 -> 2302[label="",style="dashed", color="magenta", weight=3]; 2254 -> 2303[label="",style="dashed", color="magenta", weight=3]; 4111[label="gcd2 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48) == fromInt (Pos Zero)) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];4111 -> 4132[label="",style="solid", color="black", weight=3]; 2262 -> 2305[label="",style="dashed", color="red", weight=0]; 2262[label="primQuotInt (primPlusInt (Neg (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (Neg (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="magenta"];2262 -> 2306[label="",style="dashed", color="magenta", weight=3]; 2262 -> 2307[label="",style="dashed", color="magenta", weight=3]; 2263 -> 2308[label="",style="dashed", color="red", weight=0]; 2263[label="primQuotInt (primPlusInt (Pos (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (Pos (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="magenta"];2263 -> 2309[label="",style="dashed", color="magenta", weight=3]; 2263 -> 2310[label="",style="dashed", color="magenta", weight=3]; 5718[label="gcd2 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53) == fromInt (Pos Zero)) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5718 -> 5738[label="",style="solid", color="black", weight=3]; 2288 -> 678[label="",style="dashed", color="red", weight=0]; 2288[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];2288 -> 2312[label="",style="dashed", color="magenta", weight=3]; 2288 -> 2313[label="",style="dashed", color="magenta", weight=3]; 2289 -> 678[label="",style="dashed", color="red", weight=0]; 2289[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];2289 -> 2314[label="",style="dashed", color="magenta", weight=3]; 2289 -> 2315[label="",style="dashed", color="magenta", weight=3]; 2287[label="primQuotInt (primPlusInt (Pos vuz185) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (Pos vuz186) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="triangle"];2287 -> 2316[label="",style="solid", color="black", weight=3]; 2291 -> 678[label="",style="dashed", color="red", weight=0]; 2291[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];2291 -> 2317[label="",style="dashed", color="magenta", weight=3]; 2291 -> 2318[label="",style="dashed", color="magenta", weight=3]; 2292 -> 678[label="",style="dashed", color="red", weight=0]; 2292[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];2292 -> 2319[label="",style="dashed", color="magenta", weight=3]; 2292 -> 2320[label="",style="dashed", color="magenta", weight=3]; 2290[label="primQuotInt (primPlusInt (Neg vuz187) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (Neg vuz188) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="triangle"];2290 -> 2321[label="",style="solid", color="black", weight=3]; 5733[label="gcd2 (primEqInt (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (fromInt (Pos Zero))) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5733 -> 5748[label="",style="solid", color="black", weight=3]; 5734 -> 4127[label="",style="dashed", color="red", weight=0]; 5734[label="primDivNatS vuz73 (Succ vuz34600)",fontsize=16,color="magenta"];5734 -> 5749[label="",style="dashed", color="magenta", weight=3]; 5734 -> 5750[label="",style="dashed", color="magenta", weight=3]; 5735 -> 4127[label="",style="dashed", color="red", weight=0]; 5735[label="primDivNatS vuz73 (Succ vuz34600)",fontsize=16,color="magenta"];5735 -> 5751[label="",style="dashed", color="magenta", weight=3]; 5735 -> 5752[label="",style="dashed", color="magenta", weight=3]; 2202 -> 678[label="",style="dashed", color="red", weight=0]; 2202[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];2202 -> 2323[label="",style="dashed", color="magenta", weight=3]; 2202 -> 2324[label="",style="dashed", color="magenta", weight=3]; 2203 -> 678[label="",style="dashed", color="red", weight=0]; 2203[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];2203 -> 2325[label="",style="dashed", color="magenta", weight=3]; 2203 -> 2326[label="",style="dashed", color="magenta", weight=3]; 2201[label="primQuotInt (primPlusInt (Neg vuz167) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (Neg vuz168) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="triangle"];2201 -> 2327[label="",style="solid", color="black", weight=3]; 2218 -> 678[label="",style="dashed", color="red", weight=0]; 2218[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];2218 -> 2328[label="",style="dashed", color="magenta", weight=3]; 2218 -> 2329[label="",style="dashed", color="magenta", weight=3]; 2219 -> 678[label="",style="dashed", color="red", weight=0]; 2219[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];2219 -> 2330[label="",style="dashed", color="magenta", weight=3]; 2219 -> 2331[label="",style="dashed", color="magenta", weight=3]; 2217[label="primQuotInt (primPlusInt (Pos vuz169) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (Pos vuz170) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="triangle"];2217 -> 2332[label="",style="solid", color="black", weight=3]; 4126[label="gcd2 (primEqInt (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (fromInt (Pos Zero))) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4126 -> 4142[label="",style="solid", color="black", weight=3]; 4127[label="primDivNatS vuz280 (Succ vuz28100)",fontsize=16,color="burlywood",shape="triangle"];6500[label="vuz280/Succ vuz2800",fontsize=10,color="white",style="solid",shape="box"];4127 -> 6500[label="",style="solid", color="burlywood", weight=9]; 6500 -> 4143[label="",style="solid", color="burlywood", weight=3]; 6501[label="vuz280/Zero",fontsize=10,color="white",style="solid",shape="box"];4127 -> 6501[label="",style="solid", color="burlywood", weight=9]; 6501 -> 4144[label="",style="solid", color="burlywood", weight=3]; 4128[label="error []",fontsize=16,color="red",shape="box"];4129 -> 4127[label="",style="dashed", color="red", weight=0]; 4129[label="primDivNatS vuz280 (Succ vuz28100)",fontsize=16,color="magenta"];4129 -> 4145[label="",style="dashed", color="magenta", weight=3]; 2233 -> 678[label="",style="dashed", color="red", weight=0]; 2233[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];2233 -> 2334[label="",style="dashed", color="magenta", weight=3]; 2233 -> 2335[label="",style="dashed", color="magenta", weight=3]; 2234 -> 678[label="",style="dashed", color="red", weight=0]; 2234[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];2234 -> 2336[label="",style="dashed", color="magenta", weight=3]; 2234 -> 2337[label="",style="dashed", color="magenta", weight=3]; 2232[label="primQuotInt (primPlusInt (Pos vuz171) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (Pos vuz172) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="triangle"];2232 -> 2338[label="",style="solid", color="black", weight=3]; 2246 -> 678[label="",style="dashed", color="red", weight=0]; 2246[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];2246 -> 2339[label="",style="dashed", color="magenta", weight=3]; 2246 -> 2340[label="",style="dashed", color="magenta", weight=3]; 2247 -> 678[label="",style="dashed", color="red", weight=0]; 2247[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];2247 -> 2341[label="",style="dashed", color="magenta", weight=3]; 2247 -> 2342[label="",style="dashed", color="magenta", weight=3]; 2245[label="primQuotInt (primPlusInt (Neg vuz173) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (Neg vuz174) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="triangle"];2245 -> 2343[label="",style="solid", color="black", weight=3]; 4130[label="gcd2 (primEqInt (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (fromInt (Pos Zero))) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];4130 -> 4146[label="",style="solid", color="black", weight=3]; 2258 -> 678[label="",style="dashed", color="red", weight=0]; 2258[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];2258 -> 2345[label="",style="dashed", color="magenta", weight=3]; 2258 -> 2346[label="",style="dashed", color="magenta", weight=3]; 2259 -> 678[label="",style="dashed", color="red", weight=0]; 2259[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];2259 -> 2347[label="",style="dashed", color="magenta", weight=3]; 2259 -> 2348[label="",style="dashed", color="magenta", weight=3]; 2257[label="primQuotInt (primPlusInt (Neg vuz175) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (Neg vuz176) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="triangle"];2257 -> 2349[label="",style="solid", color="black", weight=3]; 2266 -> 678[label="",style="dashed", color="red", weight=0]; 2266[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];2266 -> 2350[label="",style="dashed", color="magenta", weight=3]; 2266 -> 2351[label="",style="dashed", color="magenta", weight=3]; 2267 -> 678[label="",style="dashed", color="red", weight=0]; 2267[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];2267 -> 2352[label="",style="dashed", color="magenta", weight=3]; 2267 -> 2353[label="",style="dashed", color="magenta", weight=3]; 2265[label="primQuotInt (primPlusInt (Pos vuz177) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (Pos vuz178) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="triangle"];2265 -> 2354[label="",style="solid", color="black", weight=3]; 5736[label="gcd2 (primEqInt (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (fromInt (Pos Zero))) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5736 -> 5753[label="",style="solid", color="black", weight=3]; 2272 -> 678[label="",style="dashed", color="red", weight=0]; 2272[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];2272 -> 2356[label="",style="dashed", color="magenta", weight=3]; 2272 -> 2357[label="",style="dashed", color="magenta", weight=3]; 2273 -> 678[label="",style="dashed", color="red", weight=0]; 2273[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];2273 -> 2358[label="",style="dashed", color="magenta", weight=3]; 2273 -> 2359[label="",style="dashed", color="magenta", weight=3]; 2271[label="primQuotInt (primPlusInt (Pos vuz179) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (Pos vuz180) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="triangle"];2271 -> 2360[label="",style="solid", color="black", weight=3]; 2278 -> 678[label="",style="dashed", color="red", weight=0]; 2278[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];2278 -> 2361[label="",style="dashed", color="magenta", weight=3]; 2278 -> 2362[label="",style="dashed", color="magenta", weight=3]; 2279 -> 678[label="",style="dashed", color="red", weight=0]; 2279[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];2279 -> 2363[label="",style="dashed", color="magenta", weight=3]; 2279 -> 2364[label="",style="dashed", color="magenta", weight=3]; 2277[label="primQuotInt (primPlusInt (Neg vuz181) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (Neg vuz182) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="triangle"];2277 -> 2365[label="",style="solid", color="black", weight=3]; 5737[label="gcd2 (primEqInt (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (fromInt (Pos Zero))) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5737 -> 5754[label="",style="solid", color="black", weight=3]; 2285 -> 678[label="",style="dashed", color="red", weight=0]; 2285[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];2285 -> 2367[label="",style="dashed", color="magenta", weight=3]; 2285 -> 2368[label="",style="dashed", color="magenta", weight=3]; 2286 -> 678[label="",style="dashed", color="red", weight=0]; 2286[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];2286 -> 2369[label="",style="dashed", color="magenta", weight=3]; 2286 -> 2370[label="",style="dashed", color="magenta", weight=3]; 2284[label="primQuotInt (primPlusInt (Neg vuz183) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (Neg vuz184) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="triangle"];2284 -> 2371[label="",style="solid", color="black", weight=3]; 2295 -> 678[label="",style="dashed", color="red", weight=0]; 2295[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];2295 -> 2372[label="",style="dashed", color="magenta", weight=3]; 2295 -> 2373[label="",style="dashed", color="magenta", weight=3]; 2296 -> 678[label="",style="dashed", color="red", weight=0]; 2296[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];2296 -> 2374[label="",style="dashed", color="magenta", weight=3]; 2296 -> 2375[label="",style="dashed", color="magenta", weight=3]; 2294[label="primQuotInt (primPlusInt (Pos vuz189) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (Pos vuz190) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="triangle"];2294 -> 2376[label="",style="solid", color="black", weight=3]; 4131[label="gcd2 (primEqInt (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (fromInt (Pos Zero))) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];4131 -> 4147[label="",style="solid", color="black", weight=3]; 2299 -> 678[label="",style="dashed", color="red", weight=0]; 2299[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];2299 -> 2378[label="",style="dashed", color="magenta", weight=3]; 2299 -> 2379[label="",style="dashed", color="magenta", weight=3]; 2300 -> 678[label="",style="dashed", color="red", weight=0]; 2300[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];2300 -> 2380[label="",style="dashed", color="magenta", weight=3]; 2300 -> 2381[label="",style="dashed", color="magenta", weight=3]; 2298[label="primQuotInt (primPlusInt (Pos vuz191) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (Pos vuz192) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="triangle"];2298 -> 2382[label="",style="solid", color="black", weight=3]; 2302 -> 678[label="",style="dashed", color="red", weight=0]; 2302[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];2302 -> 2383[label="",style="dashed", color="magenta", weight=3]; 2302 -> 2384[label="",style="dashed", color="magenta", weight=3]; 2303 -> 678[label="",style="dashed", color="red", weight=0]; 2303[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];2303 -> 2385[label="",style="dashed", color="magenta", weight=3]; 2303 -> 2386[label="",style="dashed", color="magenta", weight=3]; 2301[label="primQuotInt (primPlusInt (Neg vuz193) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (Neg vuz194) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="triangle"];2301 -> 2387[label="",style="solid", color="black", weight=3]; 4132[label="gcd2 (primEqInt (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (fromInt (Pos Zero))) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];4132 -> 4148[label="",style="solid", color="black", weight=3]; 2306 -> 678[label="",style="dashed", color="red", weight=0]; 2306[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];2306 -> 2389[label="",style="dashed", color="magenta", weight=3]; 2306 -> 2390[label="",style="dashed", color="magenta", weight=3]; 2307 -> 678[label="",style="dashed", color="red", weight=0]; 2307[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];2307 -> 2391[label="",style="dashed", color="magenta", weight=3]; 2307 -> 2392[label="",style="dashed", color="magenta", weight=3]; 2305[label="primQuotInt (primPlusInt (Neg vuz195) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (Neg vuz196) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="triangle"];2305 -> 2393[label="",style="solid", color="black", weight=3]; 2309 -> 678[label="",style="dashed", color="red", weight=0]; 2309[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];2309 -> 2394[label="",style="dashed", color="magenta", weight=3]; 2309 -> 2395[label="",style="dashed", color="magenta", weight=3]; 2310 -> 678[label="",style="dashed", color="red", weight=0]; 2310[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];2310 -> 2396[label="",style="dashed", color="magenta", weight=3]; 2310 -> 2397[label="",style="dashed", color="magenta", weight=3]; 2308[label="primQuotInt (primPlusInt (Pos vuz197) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (Pos vuz198) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="triangle"];2308 -> 2398[label="",style="solid", color="black", weight=3]; 5738[label="gcd2 (primEqInt (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (fromInt (Pos Zero))) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5738 -> 5755[label="",style="solid", color="black", weight=3]; 2312[label="vuz90",fontsize=16,color="green",shape="box"];2313[label="vuz10",fontsize=16,color="green",shape="box"];2314[label="vuz90",fontsize=16,color="green",shape="box"];2315[label="vuz10",fontsize=16,color="green",shape="box"];2316[label="primQuotInt (primPlusInt (Pos vuz185) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (reduce2D (primPlusInt (Pos vuz186) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2316 -> 2400[label="",style="solid", color="black", weight=3]; 2317[label="vuz90",fontsize=16,color="green",shape="box"];2318[label="vuz10",fontsize=16,color="green",shape="box"];2319[label="vuz90",fontsize=16,color="green",shape="box"];2320[label="vuz10",fontsize=16,color="green",shape="box"];2321[label="primQuotInt (primPlusInt (Neg vuz187) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (reduce2D (primPlusInt (Neg vuz188) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2321 -> 2401[label="",style="solid", color="black", weight=3]; 5748[label="gcd2 (primEqInt (primPlusInt (vuz9 * Pos (Succ vuz10)) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (vuz9 * Pos (Succ vuz10)) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5748 -> 5767[label="",style="solid", color="black", weight=3]; 5749[label="vuz34600",fontsize=16,color="green",shape="box"];5750[label="vuz73",fontsize=16,color="green",shape="box"];5751[label="vuz34600",fontsize=16,color="green",shape="box"];5752[label="vuz73",fontsize=16,color="green",shape="box"];2323[label="vuz200",fontsize=16,color="green",shape="box"];2324[label="vuz21",fontsize=16,color="green",shape="box"];2325[label="vuz200",fontsize=16,color="green",shape="box"];2326[label="vuz21",fontsize=16,color="green",shape="box"];2327[label="primQuotInt (primPlusInt (Neg vuz167) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (reduce2D (primPlusInt (Neg vuz168) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (Neg vuz68))",fontsize=16,color="black",shape="box"];2327 -> 2404[label="",style="solid", color="black", weight=3]; 2328[label="vuz200",fontsize=16,color="green",shape="box"];2329[label="vuz21",fontsize=16,color="green",shape="box"];2330[label="vuz200",fontsize=16,color="green",shape="box"];2331[label="vuz21",fontsize=16,color="green",shape="box"];2332[label="primQuotInt (primPlusInt (Pos vuz169) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (reduce2D (primPlusInt (Pos vuz170) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (Neg vuz68))",fontsize=16,color="black",shape="box"];2332 -> 2405[label="",style="solid", color="black", weight=3]; 4142[label="gcd2 (primEqInt (primPlusInt (vuz20 * Neg (Succ vuz21)) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (vuz20 * Neg (Succ vuz21)) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4142 -> 4158[label="",style="solid", color="black", weight=3]; 4143[label="primDivNatS (Succ vuz2800) (Succ vuz28100)",fontsize=16,color="black",shape="box"];4143 -> 4159[label="",style="solid", color="black", weight=3]; 4144[label="primDivNatS Zero (Succ vuz28100)",fontsize=16,color="black",shape="box"];4144 -> 4160[label="",style="solid", color="black", weight=3]; 4145[label="vuz28100",fontsize=16,color="green",shape="box"];2334[label="vuz250",fontsize=16,color="green",shape="box"];2335[label="vuz26",fontsize=16,color="green",shape="box"];2336[label="vuz250",fontsize=16,color="green",shape="box"];2337[label="vuz26",fontsize=16,color="green",shape="box"];2338[label="primQuotInt (primPlusInt (Pos vuz171) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (reduce2D (primPlusInt (Pos vuz172) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2338 -> 2408[label="",style="solid", color="black", weight=3]; 2339[label="vuz250",fontsize=16,color="green",shape="box"];2340[label="vuz26",fontsize=16,color="green",shape="box"];2341[label="vuz250",fontsize=16,color="green",shape="box"];2342[label="vuz26",fontsize=16,color="green",shape="box"];2343[label="primQuotInt (primPlusInt (Neg vuz173) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (reduce2D (primPlusInt (Neg vuz174) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2343 -> 2409[label="",style="solid", color="black", weight=3]; 4146[label="gcd2 (primEqInt (primPlusInt (vuz25 * Pos (Succ vuz26)) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (vuz25 * Pos (Succ vuz26)) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4146 -> 4161[label="",style="solid", color="black", weight=3]; 2345[label="vuz300",fontsize=16,color="green",shape="box"];2346[label="vuz31",fontsize=16,color="green",shape="box"];2347[label="vuz300",fontsize=16,color="green",shape="box"];2348[label="vuz31",fontsize=16,color="green",shape="box"];2349[label="primQuotInt (primPlusInt (Neg vuz175) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (reduce2D (primPlusInt (Neg vuz176) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2349 -> 2412[label="",style="solid", color="black", weight=3]; 2350[label="vuz300",fontsize=16,color="green",shape="box"];2351[label="vuz31",fontsize=16,color="green",shape="box"];2352[label="vuz300",fontsize=16,color="green",shape="box"];2353[label="vuz31",fontsize=16,color="green",shape="box"];2354[label="primQuotInt (primPlusInt (Pos vuz177) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (reduce2D (primPlusInt (Pos vuz178) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2354 -> 2413[label="",style="solid", color="black", weight=3]; 5753[label="gcd2 (primEqInt (primPlusInt (vuz30 * Neg (Succ vuz31)) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (vuz30 * Neg (Succ vuz31)) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5753 -> 5768[label="",style="solid", color="black", weight=3]; 2356[label="vuz350",fontsize=16,color="green",shape="box"];2357[label="vuz36",fontsize=16,color="green",shape="box"];2358[label="vuz350",fontsize=16,color="green",shape="box"];2359[label="vuz36",fontsize=16,color="green",shape="box"];2360[label="primQuotInt (primPlusInt (Pos vuz179) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (reduce2D (primPlusInt (Pos vuz180) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2360 -> 2416[label="",style="solid", color="black", weight=3]; 2361[label="vuz350",fontsize=16,color="green",shape="box"];2362[label="vuz36",fontsize=16,color="green",shape="box"];2363[label="vuz350",fontsize=16,color="green",shape="box"];2364[label="vuz36",fontsize=16,color="green",shape="box"];2365[label="primQuotInt (primPlusInt (Neg vuz181) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (reduce2D (primPlusInt (Neg vuz182) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2365 -> 2417[label="",style="solid", color="black", weight=3]; 5754[label="gcd2 (primEqInt (primPlusInt (vuz35 * Pos (Succ vuz36)) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (vuz35 * Pos (Succ vuz36)) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5754 -> 5769[label="",style="solid", color="black", weight=3]; 2367[label="vuz400",fontsize=16,color="green",shape="box"];2368[label="vuz41",fontsize=16,color="green",shape="box"];2369[label="vuz400",fontsize=16,color="green",shape="box"];2370[label="vuz41",fontsize=16,color="green",shape="box"];2371[label="primQuotInt (primPlusInt (Neg vuz183) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (reduce2D (primPlusInt (Neg vuz184) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2371 -> 2420[label="",style="solid", color="black", weight=3]; 2372[label="vuz400",fontsize=16,color="green",shape="box"];2373[label="vuz41",fontsize=16,color="green",shape="box"];2374[label="vuz400",fontsize=16,color="green",shape="box"];2375[label="vuz41",fontsize=16,color="green",shape="box"];2376[label="primQuotInt (primPlusInt (Pos vuz189) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (reduce2D (primPlusInt (Pos vuz190) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2376 -> 2421[label="",style="solid", color="black", weight=3]; 4147[label="gcd2 (primEqInt (primPlusInt (vuz40 * Neg (Succ vuz41)) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (vuz40 * Neg (Succ vuz41)) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4147 -> 4162[label="",style="solid", color="black", weight=3]; 2378[label="vuz450",fontsize=16,color="green",shape="box"];2379[label="vuz46",fontsize=16,color="green",shape="box"];2380[label="vuz450",fontsize=16,color="green",shape="box"];2381[label="vuz46",fontsize=16,color="green",shape="box"];2382[label="primQuotInt (primPlusInt (Pos vuz191) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (reduce2D (primPlusInt (Pos vuz192) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2382 -> 2424[label="",style="solid", color="black", weight=3]; 2383[label="vuz450",fontsize=16,color="green",shape="box"];2384[label="vuz46",fontsize=16,color="green",shape="box"];2385[label="vuz450",fontsize=16,color="green",shape="box"];2386[label="vuz46",fontsize=16,color="green",shape="box"];2387[label="primQuotInt (primPlusInt (Neg vuz193) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (reduce2D (primPlusInt (Neg vuz194) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2387 -> 2425[label="",style="solid", color="black", weight=3]; 4148[label="gcd2 (primEqInt (primPlusInt (vuz45 * Pos (Succ vuz46)) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (vuz45 * Pos (Succ vuz46)) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4148 -> 4163[label="",style="solid", color="black", weight=3]; 2389[label="vuz500",fontsize=16,color="green",shape="box"];2390[label="vuz51",fontsize=16,color="green",shape="box"];2391[label="vuz500",fontsize=16,color="green",shape="box"];2392[label="vuz51",fontsize=16,color="green",shape="box"];2393[label="primQuotInt (primPlusInt (Neg vuz195) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (reduce2D (primPlusInt (Neg vuz196) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2393 -> 2428[label="",style="solid", color="black", weight=3]; 2394[label="vuz500",fontsize=16,color="green",shape="box"];2395[label="vuz51",fontsize=16,color="green",shape="box"];2396[label="vuz500",fontsize=16,color="green",shape="box"];2397[label="vuz51",fontsize=16,color="green",shape="box"];2398[label="primQuotInt (primPlusInt (Pos vuz197) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (reduce2D (primPlusInt (Pos vuz198) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2398 -> 2429[label="",style="solid", color="black", weight=3]; 5755[label="gcd2 (primEqInt (primPlusInt (vuz50 * Neg (Succ vuz51)) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (vuz50 * Neg (Succ vuz51)) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5755 -> 5770[label="",style="solid", color="black", weight=3]; 2400 -> 2432[label="",style="dashed", color="red", weight=0]; 2400[label="primQuotInt (primPlusInt (Pos vuz185) (Neg (primMulNat vuz11 (Succ vuz12)))) (reduce2D (primPlusInt (Pos vuz186) (Neg (primMulNat vuz11 (Succ vuz12)))) (Pos vuz144))",fontsize=16,color="magenta"];2400 -> 2433[label="",style="dashed", color="magenta", weight=3]; 2400 -> 2434[label="",style="dashed", color="magenta", weight=3]; 2401 -> 2440[label="",style="dashed", color="red", weight=0]; 2401[label="primQuotInt (primPlusInt (Neg vuz187) (Neg (primMulNat vuz11 (Succ vuz12)))) (reduce2D (primPlusInt (Neg vuz188) (Neg (primMulNat vuz11 (Succ vuz12)))) (Pos vuz144))",fontsize=16,color="magenta"];2401 -> 2441[label="",style="dashed", color="magenta", weight=3]; 2401 -> 2442[label="",style="dashed", color="magenta", weight=3]; 5767[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz9 (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz9 (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="burlywood",shape="box"];6502[label="vuz9/Pos vuz90",fontsize=10,color="white",style="solid",shape="box"];5767 -> 6502[label="",style="solid", color="burlywood", weight=9]; 6502 -> 5782[label="",style="solid", color="burlywood", weight=3]; 6503[label="vuz9/Neg vuz90",fontsize=10,color="white",style="solid",shape="box"];5767 -> 6503[label="",style="solid", color="burlywood", weight=9]; 6503 -> 5783[label="",style="solid", color="burlywood", weight=3]; 2404 -> 2450[label="",style="dashed", color="red", weight=0]; 2404[label="primQuotInt (primPlusInt (Neg vuz167) (Neg (primMulNat vuz22 (Succ vuz23)))) (reduce2D (primPlusInt (Neg vuz168) (Neg (primMulNat vuz22 (Succ vuz23)))) (Neg vuz68))",fontsize=16,color="magenta"];2404 -> 2451[label="",style="dashed", color="magenta", weight=3]; 2404 -> 2452[label="",style="dashed", color="magenta", weight=3]; 2405 -> 2458[label="",style="dashed", color="red", weight=0]; 2405[label="primQuotInt (primPlusInt (Pos vuz169) (Neg (primMulNat vuz22 (Succ vuz23)))) (reduce2D (primPlusInt (Pos vuz170) (Neg (primMulNat vuz22 (Succ vuz23)))) (Neg vuz68))",fontsize=16,color="magenta"];2405 -> 2459[label="",style="dashed", color="magenta", weight=3]; 2405 -> 2460[label="",style="dashed", color="magenta", weight=3]; 4158[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz20 (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz20 (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="burlywood",shape="box"];6504[label="vuz20/Pos vuz200",fontsize=10,color="white",style="solid",shape="box"];4158 -> 6504[label="",style="solid", color="burlywood", weight=9]; 6504 -> 4173[label="",style="solid", color="burlywood", weight=3]; 6505[label="vuz20/Neg vuz200",fontsize=10,color="white",style="solid",shape="box"];4158 -> 6505[label="",style="solid", color="burlywood", weight=9]; 6505 -> 4174[label="",style="solid", color="burlywood", weight=3]; 4159[label="primDivNatS0 vuz2800 vuz28100 (primGEqNatS vuz2800 vuz28100)",fontsize=16,color="burlywood",shape="box"];6506[label="vuz2800/Succ vuz28000",fontsize=10,color="white",style="solid",shape="box"];4159 -> 6506[label="",style="solid", color="burlywood", weight=9]; 6506 -> 4175[label="",style="solid", color="burlywood", weight=3]; 6507[label="vuz2800/Zero",fontsize=10,color="white",style="solid",shape="box"];4159 -> 6507[label="",style="solid", color="burlywood", weight=9]; 6507 -> 4176[label="",style="solid", color="burlywood", weight=3]; 4160[label="Zero",fontsize=16,color="green",shape="box"];2408 -> 2468[label="",style="dashed", color="red", weight=0]; 2408[label="primQuotInt (primPlusInt (Pos vuz171) (Pos (primMulNat vuz27 (Succ vuz28)))) (reduce2D (primPlusInt (Pos vuz172) (Pos (primMulNat vuz27 (Succ vuz28)))) (Neg vuz71))",fontsize=16,color="magenta"];2408 -> 2469[label="",style="dashed", color="magenta", weight=3]; 2408 -> 2470[label="",style="dashed", color="magenta", weight=3]; 2409 -> 2476[label="",style="dashed", color="red", weight=0]; 2409[label="primQuotInt (primPlusInt (Neg vuz173) (Pos (primMulNat vuz27 (Succ vuz28)))) (reduce2D (primPlusInt (Neg vuz174) (Pos (primMulNat vuz27 (Succ vuz28)))) (Neg vuz71))",fontsize=16,color="magenta"];2409 -> 2477[label="",style="dashed", color="magenta", weight=3]; 2409 -> 2478[label="",style="dashed", color="magenta", weight=3]; 4161[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz25 (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz25 (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="burlywood",shape="box"];6508[label="vuz25/Pos vuz250",fontsize=10,color="white",style="solid",shape="box"];4161 -> 6508[label="",style="solid", color="burlywood", weight=9]; 6508 -> 4177[label="",style="solid", color="burlywood", weight=3]; 6509[label="vuz25/Neg vuz250",fontsize=10,color="white",style="solid",shape="box"];4161 -> 6509[label="",style="solid", color="burlywood", weight=9]; 6509 -> 4178[label="",style="solid", color="burlywood", weight=3]; 2412 -> 2486[label="",style="dashed", color="red", weight=0]; 2412[label="primQuotInt (primPlusInt (Neg vuz175) (Pos (primMulNat vuz32 (Succ vuz33)))) (reduce2D (primPlusInt (Neg vuz176) (Pos (primMulNat vuz32 (Succ vuz33)))) (Pos vuz74))",fontsize=16,color="magenta"];2412 -> 2487[label="",style="dashed", color="magenta", weight=3]; 2412 -> 2488[label="",style="dashed", color="magenta", weight=3]; 2413 -> 2494[label="",style="dashed", color="red", weight=0]; 2413[label="primQuotInt (primPlusInt (Pos vuz177) (Pos (primMulNat vuz32 (Succ vuz33)))) (reduce2D (primPlusInt (Pos vuz178) (Pos (primMulNat vuz32 (Succ vuz33)))) (Pos vuz74))",fontsize=16,color="magenta"];2413 -> 2495[label="",style="dashed", color="magenta", weight=3]; 2413 -> 2496[label="",style="dashed", color="magenta", weight=3]; 5768[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz30 (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz30 (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="burlywood",shape="box"];6510[label="vuz30/Pos vuz300",fontsize=10,color="white",style="solid",shape="box"];5768 -> 6510[label="",style="solid", color="burlywood", weight=9]; 6510 -> 5784[label="",style="solid", color="burlywood", weight=3]; 6511[label="vuz30/Neg vuz300",fontsize=10,color="white",style="solid",shape="box"];5768 -> 6511[label="",style="solid", color="burlywood", weight=9]; 6511 -> 5785[label="",style="solid", color="burlywood", weight=3]; 2416 -> 2494[label="",style="dashed", color="red", weight=0]; 2416[label="primQuotInt (primPlusInt (Pos vuz179) (Pos (primMulNat vuz37 (Succ vuz38)))) (reduce2D (primPlusInt (Pos vuz180) (Pos (primMulNat vuz37 (Succ vuz38)))) (Pos vuz77))",fontsize=16,color="magenta"];2416 -> 2497[label="",style="dashed", color="magenta", weight=3]; 2416 -> 2498[label="",style="dashed", color="magenta", weight=3]; 2416 -> 2499[label="",style="dashed", color="magenta", weight=3]; 2416 -> 2500[label="",style="dashed", color="magenta", weight=3]; 2416 -> 2501[label="",style="dashed", color="magenta", weight=3]; 2417 -> 2486[label="",style="dashed", color="red", weight=0]; 2417[label="primQuotInt (primPlusInt (Neg vuz181) (Pos (primMulNat vuz37 (Succ vuz38)))) (reduce2D (primPlusInt (Neg vuz182) (Pos (primMulNat vuz37 (Succ vuz38)))) (Pos vuz77))",fontsize=16,color="magenta"];2417 -> 2489[label="",style="dashed", color="magenta", weight=3]; 2417 -> 2490[label="",style="dashed", color="magenta", weight=3]; 2417 -> 2491[label="",style="dashed", color="magenta", weight=3]; 2417 -> 2492[label="",style="dashed", color="magenta", weight=3]; 2417 -> 2493[label="",style="dashed", color="magenta", weight=3]; 5769[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz35 (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz35 (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="burlywood",shape="box"];6512[label="vuz35/Pos vuz350",fontsize=10,color="white",style="solid",shape="box"];5769 -> 6512[label="",style="solid", color="burlywood", weight=9]; 6512 -> 5786[label="",style="solid", color="burlywood", weight=3]; 6513[label="vuz35/Neg vuz350",fontsize=10,color="white",style="solid",shape="box"];5769 -> 6513[label="",style="solid", color="burlywood", weight=9]; 6513 -> 5787[label="",style="solid", color="burlywood", weight=3]; 2420 -> 2476[label="",style="dashed", color="red", weight=0]; 2420[label="primQuotInt (primPlusInt (Neg vuz183) (Pos (primMulNat vuz42 (Succ vuz43)))) (reduce2D (primPlusInt (Neg vuz184) (Pos (primMulNat vuz42 (Succ vuz43)))) (Neg vuz92))",fontsize=16,color="magenta"];2420 -> 2479[label="",style="dashed", color="magenta", weight=3]; 2420 -> 2480[label="",style="dashed", color="magenta", weight=3]; 2420 -> 2481[label="",style="dashed", color="magenta", weight=3]; 2420 -> 2482[label="",style="dashed", color="magenta", weight=3]; 2420 -> 2483[label="",style="dashed", color="magenta", weight=3]; 2421 -> 2468[label="",style="dashed", color="red", weight=0]; 2421[label="primQuotInt (primPlusInt (Pos vuz189) (Pos (primMulNat vuz42 (Succ vuz43)))) (reduce2D (primPlusInt (Pos vuz190) (Pos (primMulNat vuz42 (Succ vuz43)))) (Neg vuz92))",fontsize=16,color="magenta"];2421 -> 2471[label="",style="dashed", color="magenta", weight=3]; 2421 -> 2472[label="",style="dashed", color="magenta", weight=3]; 2421 -> 2473[label="",style="dashed", color="magenta", weight=3]; 2421 -> 2474[label="",style="dashed", color="magenta", weight=3]; 2421 -> 2475[label="",style="dashed", color="magenta", weight=3]; 4162[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz40 (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz40 (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="burlywood",shape="box"];6514[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];4162 -> 6514[label="",style="solid", color="burlywood", weight=9]; 6514 -> 4179[label="",style="solid", color="burlywood", weight=3]; 6515[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];4162 -> 6515[label="",style="solid", color="burlywood", weight=9]; 6515 -> 4180[label="",style="solid", color="burlywood", weight=3]; 2424 -> 2458[label="",style="dashed", color="red", weight=0]; 2424[label="primQuotInt (primPlusInt (Pos vuz191) (Neg (primMulNat vuz47 (Succ vuz48)))) (reduce2D (primPlusInt (Pos vuz192) (Neg (primMulNat vuz47 (Succ vuz48)))) (Neg vuz107))",fontsize=16,color="magenta"];2424 -> 2461[label="",style="dashed", color="magenta", weight=3]; 2424 -> 2462[label="",style="dashed", color="magenta", weight=3]; 2424 -> 2463[label="",style="dashed", color="magenta", weight=3]; 2424 -> 2464[label="",style="dashed", color="magenta", weight=3]; 2424 -> 2465[label="",style="dashed", color="magenta", weight=3]; 2425 -> 2450[label="",style="dashed", color="red", weight=0]; 2425[label="primQuotInt (primPlusInt (Neg vuz193) (Neg (primMulNat vuz47 (Succ vuz48)))) (reduce2D (primPlusInt (Neg vuz194) (Neg (primMulNat vuz47 (Succ vuz48)))) (Neg vuz107))",fontsize=16,color="magenta"];2425 -> 2453[label="",style="dashed", color="magenta", weight=3]; 2425 -> 2454[label="",style="dashed", color="magenta", weight=3]; 2425 -> 2455[label="",style="dashed", color="magenta", weight=3]; 2425 -> 2456[label="",style="dashed", color="magenta", weight=3]; 2425 -> 2457[label="",style="dashed", color="magenta", weight=3]; 4163[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz45 (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz45 (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="burlywood",shape="box"];6516[label="vuz45/Pos vuz450",fontsize=10,color="white",style="solid",shape="box"];4163 -> 6516[label="",style="solid", color="burlywood", weight=9]; 6516 -> 4181[label="",style="solid", color="burlywood", weight=3]; 6517[label="vuz45/Neg vuz450",fontsize=10,color="white",style="solid",shape="box"];4163 -> 6517[label="",style="solid", color="burlywood", weight=9]; 6517 -> 4182[label="",style="solid", color="burlywood", weight=3]; 2428 -> 2440[label="",style="dashed", color="red", weight=0]; 2428[label="primQuotInt (primPlusInt (Neg vuz195) (Neg (primMulNat vuz52 (Succ vuz53)))) (reduce2D (primPlusInt (Neg vuz196) (Neg (primMulNat vuz52 (Succ vuz53)))) (Pos vuz122))",fontsize=16,color="magenta"];2428 -> 2443[label="",style="dashed", color="magenta", weight=3]; 2428 -> 2444[label="",style="dashed", color="magenta", weight=3]; 2428 -> 2445[label="",style="dashed", color="magenta", weight=3]; 2428 -> 2446[label="",style="dashed", color="magenta", weight=3]; 2428 -> 2447[label="",style="dashed", color="magenta", weight=3]; 2429 -> 2432[label="",style="dashed", color="red", weight=0]; 2429[label="primQuotInt (primPlusInt (Pos vuz197) (Neg (primMulNat vuz52 (Succ vuz53)))) (reduce2D (primPlusInt (Pos vuz198) (Neg (primMulNat vuz52 (Succ vuz53)))) (Pos vuz122))",fontsize=16,color="magenta"];2429 -> 2435[label="",style="dashed", color="magenta", weight=3]; 2429 -> 2436[label="",style="dashed", color="magenta", weight=3]; 2429 -> 2437[label="",style="dashed", color="magenta", weight=3]; 2429 -> 2438[label="",style="dashed", color="magenta", weight=3]; 2429 -> 2439[label="",style="dashed", color="magenta", weight=3]; 5770[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz50 (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz50 (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="burlywood",shape="box"];6518[label="vuz50/Pos vuz500",fontsize=10,color="white",style="solid",shape="box"];5770 -> 6518[label="",style="solid", color="burlywood", weight=9]; 6518 -> 5788[label="",style="solid", color="burlywood", weight=3]; 6519[label="vuz50/Neg vuz500",fontsize=10,color="white",style="solid",shape="box"];5770 -> 6519[label="",style="solid", color="burlywood", weight=9]; 6519 -> 5789[label="",style="solid", color="burlywood", weight=3]; 2433 -> 678[label="",style="dashed", color="red", weight=0]; 2433[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];2433 -> 2512[label="",style="dashed", color="magenta", weight=3]; 2433 -> 2513[label="",style="dashed", color="magenta", weight=3]; 2434 -> 678[label="",style="dashed", color="red", weight=0]; 2434[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];2434 -> 2514[label="",style="dashed", color="magenta", weight=3]; 2434 -> 2515[label="",style="dashed", color="magenta", weight=3]; 2432[label="primQuotInt (primPlusInt (Pos vuz185) (Neg vuz199)) (reduce2D (primPlusInt (Pos vuz186) (Neg vuz200)) (Pos vuz144))",fontsize=16,color="black",shape="triangle"];2432 -> 2516[label="",style="solid", color="black", weight=3]; 2441 -> 678[label="",style="dashed", color="red", weight=0]; 2441[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];2441 -> 2517[label="",style="dashed", color="magenta", weight=3]; 2441 -> 2518[label="",style="dashed", color="magenta", weight=3]; 2442 -> 678[label="",style="dashed", color="red", weight=0]; 2442[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];2442 -> 2519[label="",style="dashed", color="magenta", weight=3]; 2442 -> 2520[label="",style="dashed", color="magenta", weight=3]; 2440[label="primQuotInt (primPlusInt (Neg vuz187) (Neg vuz201)) (reduce2D (primPlusInt (Neg vuz188) (Neg vuz202)) (Pos vuz144))",fontsize=16,color="black",shape="triangle"];2440 -> 2521[label="",style="solid", color="black", weight=3]; 5782[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5782 -> 5804[label="",style="solid", color="black", weight=3]; 5783[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5783 -> 5805[label="",style="solid", color="black", weight=3]; 2451 -> 678[label="",style="dashed", color="red", weight=0]; 2451[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];2451 -> 2528[label="",style="dashed", color="magenta", weight=3]; 2451 -> 2529[label="",style="dashed", color="magenta", weight=3]; 2452 -> 678[label="",style="dashed", color="red", weight=0]; 2452[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];2452 -> 2530[label="",style="dashed", color="magenta", weight=3]; 2452 -> 2531[label="",style="dashed", color="magenta", weight=3]; 2450[label="primQuotInt (primPlusInt (Neg vuz167) (Neg vuz203)) (reduce2D (primPlusInt (Neg vuz168) (Neg vuz204)) (Neg vuz68))",fontsize=16,color="black",shape="triangle"];2450 -> 2532[label="",style="solid", color="black", weight=3]; 2459 -> 678[label="",style="dashed", color="red", weight=0]; 2459[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];2459 -> 2533[label="",style="dashed", color="magenta", weight=3]; 2459 -> 2534[label="",style="dashed", color="magenta", weight=3]; 2460 -> 678[label="",style="dashed", color="red", weight=0]; 2460[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];2460 -> 2535[label="",style="dashed", color="magenta", weight=3]; 2460 -> 2536[label="",style="dashed", color="magenta", weight=3]; 2458[label="primQuotInt (primPlusInt (Pos vuz169) (Neg vuz205)) (reduce2D (primPlusInt (Pos vuz170) (Neg vuz206)) (Neg vuz68))",fontsize=16,color="black",shape="triangle"];2458 -> 2537[label="",style="solid", color="black", weight=3]; 4173[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4173 -> 4192[label="",style="solid", color="black", weight=3]; 4174[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4174 -> 4193[label="",style="solid", color="black", weight=3]; 4175[label="primDivNatS0 (Succ vuz28000) vuz28100 (primGEqNatS (Succ vuz28000) vuz28100)",fontsize=16,color="burlywood",shape="box"];6520[label="vuz28100/Succ vuz281000",fontsize=10,color="white",style="solid",shape="box"];4175 -> 6520[label="",style="solid", color="burlywood", weight=9]; 6520 -> 4194[label="",style="solid", color="burlywood", weight=3]; 6521[label="vuz28100/Zero",fontsize=10,color="white",style="solid",shape="box"];4175 -> 6521[label="",style="solid", color="burlywood", weight=9]; 6521 -> 4195[label="",style="solid", color="burlywood", weight=3]; 4176[label="primDivNatS0 Zero vuz28100 (primGEqNatS Zero vuz28100)",fontsize=16,color="burlywood",shape="box"];6522[label="vuz28100/Succ vuz281000",fontsize=10,color="white",style="solid",shape="box"];4176 -> 6522[label="",style="solid", color="burlywood", weight=9]; 6522 -> 4196[label="",style="solid", color="burlywood", weight=3]; 6523[label="vuz28100/Zero",fontsize=10,color="white",style="solid",shape="box"];4176 -> 6523[label="",style="solid", color="burlywood", weight=9]; 6523 -> 4197[label="",style="solid", color="burlywood", weight=3]; 2469 -> 678[label="",style="dashed", color="red", weight=0]; 2469[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];2469 -> 2544[label="",style="dashed", color="magenta", weight=3]; 2469 -> 2545[label="",style="dashed", color="magenta", weight=3]; 2470 -> 678[label="",style="dashed", color="red", weight=0]; 2470[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];2470 -> 2546[label="",style="dashed", color="magenta", weight=3]; 2470 -> 2547[label="",style="dashed", color="magenta", weight=3]; 2468[label="primQuotInt (primPlusInt (Pos vuz171) (Pos vuz207)) (reduce2D (primPlusInt (Pos vuz172) (Pos vuz208)) (Neg vuz71))",fontsize=16,color="black",shape="triangle"];2468 -> 2548[label="",style="solid", color="black", weight=3]; 2477 -> 678[label="",style="dashed", color="red", weight=0]; 2477[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];2477 -> 2549[label="",style="dashed", color="magenta", weight=3]; 2477 -> 2550[label="",style="dashed", color="magenta", weight=3]; 2478 -> 678[label="",style="dashed", color="red", weight=0]; 2478[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];2478 -> 2551[label="",style="dashed", color="magenta", weight=3]; 2478 -> 2552[label="",style="dashed", color="magenta", weight=3]; 2476[label="primQuotInt (primPlusInt (Neg vuz173) (Pos vuz209)) (reduce2D (primPlusInt (Neg vuz174) (Pos vuz210)) (Neg vuz71))",fontsize=16,color="black",shape="triangle"];2476 -> 2553[label="",style="solid", color="black", weight=3]; 4177[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4177 -> 4198[label="",style="solid", color="black", weight=3]; 4178[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4178 -> 4199[label="",style="solid", color="black", weight=3]; 2487 -> 678[label="",style="dashed", color="red", weight=0]; 2487[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];2487 -> 2560[label="",style="dashed", color="magenta", weight=3]; 2487 -> 2561[label="",style="dashed", color="magenta", weight=3]; 2488 -> 678[label="",style="dashed", color="red", weight=0]; 2488[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];2488 -> 2562[label="",style="dashed", color="magenta", weight=3]; 2488 -> 2563[label="",style="dashed", color="magenta", weight=3]; 2486[label="primQuotInt (primPlusInt (Neg vuz175) (Pos vuz211)) (reduce2D (primPlusInt (Neg vuz176) (Pos vuz212)) (Pos vuz74))",fontsize=16,color="black",shape="triangle"];2486 -> 2564[label="",style="solid", color="black", weight=3]; 2495 -> 678[label="",style="dashed", color="red", weight=0]; 2495[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];2495 -> 2565[label="",style="dashed", color="magenta", weight=3]; 2495 -> 2566[label="",style="dashed", color="magenta", weight=3]; 2496 -> 678[label="",style="dashed", color="red", weight=0]; 2496[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];2496 -> 2567[label="",style="dashed", color="magenta", weight=3]; 2496 -> 2568[label="",style="dashed", color="magenta", weight=3]; 2494[label="primQuotInt (primPlusInt (Pos vuz177) (Pos vuz213)) (reduce2D (primPlusInt (Pos vuz178) (Pos vuz214)) (Pos vuz74))",fontsize=16,color="black",shape="triangle"];2494 -> 2569[label="",style="solid", color="black", weight=3]; 5784[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5784 -> 5806[label="",style="solid", color="black", weight=3]; 5785[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5785 -> 5807[label="",style="solid", color="black", weight=3]; 2497 -> 678[label="",style="dashed", color="red", weight=0]; 2497[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];2497 -> 2576[label="",style="dashed", color="magenta", weight=3]; 2497 -> 2577[label="",style="dashed", color="magenta", weight=3]; 2498[label="vuz77",fontsize=16,color="green",shape="box"];2499[label="vuz179",fontsize=16,color="green",shape="box"];2500[label="vuz180",fontsize=16,color="green",shape="box"];2501 -> 678[label="",style="dashed", color="red", weight=0]; 2501[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];2501 -> 2578[label="",style="dashed", color="magenta", weight=3]; 2501 -> 2579[label="",style="dashed", color="magenta", weight=3]; 2489 -> 678[label="",style="dashed", color="red", weight=0]; 2489[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];2489 -> 2580[label="",style="dashed", color="magenta", weight=3]; 2489 -> 2581[label="",style="dashed", color="magenta", weight=3]; 2490[label="vuz182",fontsize=16,color="green",shape="box"];2491[label="vuz77",fontsize=16,color="green",shape="box"];2492 -> 678[label="",style="dashed", color="red", weight=0]; 2492[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];2492 -> 2582[label="",style="dashed", color="magenta", weight=3]; 2492 -> 2583[label="",style="dashed", color="magenta", weight=3]; 2493[label="vuz181",fontsize=16,color="green",shape="box"];5786[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5786 -> 5808[label="",style="solid", color="black", weight=3]; 5787[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5787 -> 5809[label="",style="solid", color="black", weight=3]; 2479 -> 678[label="",style="dashed", color="red", weight=0]; 2479[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];2479 -> 2590[label="",style="dashed", color="magenta", weight=3]; 2479 -> 2591[label="",style="dashed", color="magenta", weight=3]; 2480[label="vuz92",fontsize=16,color="green",shape="box"];2481[label="vuz183",fontsize=16,color="green",shape="box"];2482 -> 678[label="",style="dashed", color="red", weight=0]; 2482[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];2482 -> 2592[label="",style="dashed", color="magenta", weight=3]; 2482 -> 2593[label="",style="dashed", color="magenta", weight=3]; 2483[label="vuz184",fontsize=16,color="green",shape="box"];2471[label="vuz190",fontsize=16,color="green",shape="box"];2472[label="vuz189",fontsize=16,color="green",shape="box"];2473[label="vuz92",fontsize=16,color="green",shape="box"];2474 -> 678[label="",style="dashed", color="red", weight=0]; 2474[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];2474 -> 2594[label="",style="dashed", color="magenta", weight=3]; 2474 -> 2595[label="",style="dashed", color="magenta", weight=3]; 2475 -> 678[label="",style="dashed", color="red", weight=0]; 2475[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];2475 -> 2596[label="",style="dashed", color="magenta", weight=3]; 2475 -> 2597[label="",style="dashed", color="magenta", weight=3]; 4179[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4179 -> 4200[label="",style="solid", color="black", weight=3]; 4180[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4180 -> 4201[label="",style="solid", color="black", weight=3]; 2461[label="vuz192",fontsize=16,color="green",shape="box"];2462 -> 678[label="",style="dashed", color="red", weight=0]; 2462[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];2462 -> 2604[label="",style="dashed", color="magenta", weight=3]; 2462 -> 2605[label="",style="dashed", color="magenta", weight=3]; 2463 -> 678[label="",style="dashed", color="red", weight=0]; 2463[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];2463 -> 2606[label="",style="dashed", color="magenta", weight=3]; 2463 -> 2607[label="",style="dashed", color="magenta", weight=3]; 2464[label="vuz107",fontsize=16,color="green",shape="box"];2465[label="vuz191",fontsize=16,color="green",shape="box"];2453 -> 678[label="",style="dashed", color="red", weight=0]; 2453[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];2453 -> 2608[label="",style="dashed", color="magenta", weight=3]; 2453 -> 2609[label="",style="dashed", color="magenta", weight=3]; 2454[label="vuz194",fontsize=16,color="green",shape="box"];2455[label="vuz193",fontsize=16,color="green",shape="box"];2456[label="vuz107",fontsize=16,color="green",shape="box"];2457 -> 678[label="",style="dashed", color="red", weight=0]; 2457[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];2457 -> 2610[label="",style="dashed", color="magenta", weight=3]; 2457 -> 2611[label="",style="dashed", color="magenta", weight=3]; 4181[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4181 -> 4202[label="",style="solid", color="black", weight=3]; 4182[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4182 -> 4203[label="",style="solid", color="black", weight=3]; 2443 -> 678[label="",style="dashed", color="red", weight=0]; 2443[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];2443 -> 2618[label="",style="dashed", color="magenta", weight=3]; 2443 -> 2619[label="",style="dashed", color="magenta", weight=3]; 2444[label="vuz196",fontsize=16,color="green",shape="box"];2445[label="vuz195",fontsize=16,color="green",shape="box"];2446 -> 678[label="",style="dashed", color="red", weight=0]; 2446[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];2446 -> 2620[label="",style="dashed", color="magenta", weight=3]; 2446 -> 2621[label="",style="dashed", color="magenta", weight=3]; 2447[label="vuz122",fontsize=16,color="green",shape="box"];2435[label="vuz198",fontsize=16,color="green",shape="box"];2436 -> 678[label="",style="dashed", color="red", weight=0]; 2436[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];2436 -> 2622[label="",style="dashed", color="magenta", weight=3]; 2436 -> 2623[label="",style="dashed", color="magenta", weight=3]; 2437 -> 678[label="",style="dashed", color="red", weight=0]; 2437[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];2437 -> 2624[label="",style="dashed", color="magenta", weight=3]; 2437 -> 2625[label="",style="dashed", color="magenta", weight=3]; 2438[label="vuz122",fontsize=16,color="green",shape="box"];2439[label="vuz197",fontsize=16,color="green",shape="box"];5788[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5788 -> 5810[label="",style="solid", color="black", weight=3]; 5789[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5789 -> 5811[label="",style="solid", color="black", weight=3]; 2512[label="vuz11",fontsize=16,color="green",shape="box"];2513[label="vuz12",fontsize=16,color="green",shape="box"];2514[label="vuz11",fontsize=16,color="green",shape="box"];2515[label="vuz12",fontsize=16,color="green",shape="box"];2516[label="primQuotInt (primMinusNat vuz185 vuz199) (reduce2D (primMinusNat vuz185 vuz199) (Pos vuz144))",fontsize=16,color="burlywood",shape="triangle"];6524[label="vuz185/Succ vuz1850",fontsize=10,color="white",style="solid",shape="box"];2516 -> 6524[label="",style="solid", color="burlywood", weight=9]; 6524 -> 2632[label="",style="solid", color="burlywood", weight=3]; 6525[label="vuz185/Zero",fontsize=10,color="white",style="solid",shape="box"];2516 -> 6525[label="",style="solid", color="burlywood", weight=9]; 6525 -> 2633[label="",style="solid", color="burlywood", weight=3]; 2517[label="vuz11",fontsize=16,color="green",shape="box"];2518[label="vuz12",fontsize=16,color="green",shape="box"];2519[label="vuz11",fontsize=16,color="green",shape="box"];2520[label="vuz12",fontsize=16,color="green",shape="box"];2521 -> 3507[label="",style="dashed", color="red", weight=0]; 2521[label="primQuotInt (Neg (primPlusNat vuz187 vuz201)) (reduce2D (Neg (primPlusNat vuz187 vuz201)) (Pos vuz144))",fontsize=16,color="magenta"];2521 -> 3580[label="",style="dashed", color="magenta", weight=3]; 2521 -> 3581[label="",style="dashed", color="magenta", weight=3]; 5804 -> 5824[label="",style="dashed", color="red", weight=0]; 5804[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="magenta"];5804 -> 5825[label="",style="dashed", color="magenta", weight=3]; 5804 -> 5826[label="",style="dashed", color="magenta", weight=3]; 5805 -> 5827[label="",style="dashed", color="red", weight=0]; 5805[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="magenta"];5805 -> 5828[label="",style="dashed", color="magenta", weight=3]; 5805 -> 5829[label="",style="dashed", color="magenta", weight=3]; 2528[label="vuz22",fontsize=16,color="green",shape="box"];2529[label="vuz23",fontsize=16,color="green",shape="box"];2530[label="vuz22",fontsize=16,color="green",shape="box"];2531[label="vuz23",fontsize=16,color="green",shape="box"];2532 -> 3507[label="",style="dashed", color="red", weight=0]; 2532[label="primQuotInt (Neg (primPlusNat vuz167 vuz203)) (reduce2D (Neg (primPlusNat vuz167 vuz203)) (Neg vuz68))",fontsize=16,color="magenta"];2532 -> 3582[label="",style="dashed", color="magenta", weight=3]; 2532 -> 3583[label="",style="dashed", color="magenta", weight=3]; 2533[label="vuz22",fontsize=16,color="green",shape="box"];2534[label="vuz23",fontsize=16,color="green",shape="box"];2535[label="vuz22",fontsize=16,color="green",shape="box"];2536[label="vuz23",fontsize=16,color="green",shape="box"];2537[label="primQuotInt (primMinusNat vuz169 vuz205) (reduce2D (primMinusNat vuz169 vuz205) (Neg vuz68))",fontsize=16,color="burlywood",shape="triangle"];6526[label="vuz169/Succ vuz1690",fontsize=10,color="white",style="solid",shape="box"];2537 -> 6526[label="",style="solid", color="burlywood", weight=9]; 6526 -> 2650[label="",style="solid", color="burlywood", weight=3]; 6527[label="vuz169/Zero",fontsize=10,color="white",style="solid",shape="box"];2537 -> 6527[label="",style="solid", color="burlywood", weight=9]; 6527 -> 2651[label="",style="solid", color="burlywood", weight=3]; 4192 -> 4214[label="",style="dashed", color="red", weight=0]; 4192[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="magenta"];4192 -> 4215[label="",style="dashed", color="magenta", weight=3]; 4192 -> 4216[label="",style="dashed", color="magenta", weight=3]; 4193 -> 4217[label="",style="dashed", color="red", weight=0]; 4193[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="magenta"];4193 -> 4218[label="",style="dashed", color="magenta", weight=3]; 4193 -> 4219[label="",style="dashed", color="magenta", weight=3]; 4194[label="primDivNatS0 (Succ vuz28000) (Succ vuz281000) (primGEqNatS (Succ vuz28000) (Succ vuz281000))",fontsize=16,color="black",shape="box"];4194 -> 4220[label="",style="solid", color="black", weight=3]; 4195[label="primDivNatS0 (Succ vuz28000) Zero (primGEqNatS (Succ vuz28000) Zero)",fontsize=16,color="black",shape="box"];4195 -> 4221[label="",style="solid", color="black", weight=3]; 4196[label="primDivNatS0 Zero (Succ vuz281000) (primGEqNatS Zero (Succ vuz281000))",fontsize=16,color="black",shape="box"];4196 -> 4222[label="",style="solid", color="black", weight=3]; 4197[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];4197 -> 4223[label="",style="solid", color="black", weight=3]; 2544[label="vuz27",fontsize=16,color="green",shape="box"];2545[label="vuz28",fontsize=16,color="green",shape="box"];2546[label="vuz27",fontsize=16,color="green",shape="box"];2547[label="vuz28",fontsize=16,color="green",shape="box"];2548 -> 5044[label="",style="dashed", color="red", weight=0]; 2548[label="primQuotInt (Pos (primPlusNat vuz171 vuz207)) (reduce2D (Pos (primPlusNat vuz171 vuz207)) (Neg vuz71))",fontsize=16,color="magenta"];2548 -> 5112[label="",style="dashed", color="magenta", weight=3]; 2548 -> 5113[label="",style="dashed", color="magenta", weight=3]; 2549[label="vuz27",fontsize=16,color="green",shape="box"];2550[label="vuz28",fontsize=16,color="green",shape="box"];2551[label="vuz27",fontsize=16,color="green",shape="box"];2552[label="vuz28",fontsize=16,color="green",shape="box"];2553 -> 2537[label="",style="dashed", color="red", weight=0]; 2553[label="primQuotInt (primMinusNat vuz209 vuz173) (reduce2D (primMinusNat vuz209 vuz173) (Neg vuz71))",fontsize=16,color="magenta"];2553 -> 2665[label="",style="dashed", color="magenta", weight=3]; 2553 -> 2666[label="",style="dashed", color="magenta", weight=3]; 2553 -> 2667[label="",style="dashed", color="magenta", weight=3]; 4198 -> 4224[label="",style="dashed", color="red", weight=0]; 4198[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="magenta"];4198 -> 4225[label="",style="dashed", color="magenta", weight=3]; 4198 -> 4226[label="",style="dashed", color="magenta", weight=3]; 4199 -> 4227[label="",style="dashed", color="red", weight=0]; 4199[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="magenta"];4199 -> 4228[label="",style="dashed", color="magenta", weight=3]; 4199 -> 4229[label="",style="dashed", color="magenta", weight=3]; 2560[label="vuz32",fontsize=16,color="green",shape="box"];2561[label="vuz33",fontsize=16,color="green",shape="box"];2562[label="vuz32",fontsize=16,color="green",shape="box"];2563[label="vuz33",fontsize=16,color="green",shape="box"];2564 -> 2516[label="",style="dashed", color="red", weight=0]; 2564[label="primQuotInt (primMinusNat vuz211 vuz175) (reduce2D (primMinusNat vuz211 vuz175) (Pos vuz74))",fontsize=16,color="magenta"];2564 -> 2678[label="",style="dashed", color="magenta", weight=3]; 2564 -> 2679[label="",style="dashed", color="magenta", weight=3]; 2564 -> 2680[label="",style="dashed", color="magenta", weight=3]; 2565[label="vuz32",fontsize=16,color="green",shape="box"];2566[label="vuz33",fontsize=16,color="green",shape="box"];2567[label="vuz32",fontsize=16,color="green",shape="box"];2568[label="vuz33",fontsize=16,color="green",shape="box"];2569 -> 5044[label="",style="dashed", color="red", weight=0]; 2569[label="primQuotInt (Pos (primPlusNat vuz177 vuz213)) (reduce2D (Pos (primPlusNat vuz177 vuz213)) (Pos vuz74))",fontsize=16,color="magenta"];2569 -> 5114[label="",style="dashed", color="magenta", weight=3]; 2569 -> 5115[label="",style="dashed", color="magenta", weight=3]; 5806 -> 5830[label="",style="dashed", color="red", weight=0]; 5806[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="magenta"];5806 -> 5831[label="",style="dashed", color="magenta", weight=3]; 5806 -> 5832[label="",style="dashed", color="magenta", weight=3]; 5807 -> 5833[label="",style="dashed", color="red", weight=0]; 5807[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="magenta"];5807 -> 5834[label="",style="dashed", color="magenta", weight=3]; 5807 -> 5835[label="",style="dashed", color="magenta", weight=3]; 2576[label="vuz37",fontsize=16,color="green",shape="box"];2577[label="vuz38",fontsize=16,color="green",shape="box"];2578[label="vuz37",fontsize=16,color="green",shape="box"];2579[label="vuz38",fontsize=16,color="green",shape="box"];2580[label="vuz37",fontsize=16,color="green",shape="box"];2581[label="vuz38",fontsize=16,color="green",shape="box"];2582[label="vuz37",fontsize=16,color="green",shape="box"];2583[label="vuz38",fontsize=16,color="green",shape="box"];5808 -> 5836[label="",style="dashed", color="red", weight=0]; 5808[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="magenta"];5808 -> 5837[label="",style="dashed", color="magenta", weight=3]; 5808 -> 5838[label="",style="dashed", color="magenta", weight=3]; 5809 -> 5839[label="",style="dashed", color="red", weight=0]; 5809[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="magenta"];5809 -> 5840[label="",style="dashed", color="magenta", weight=3]; 5809 -> 5841[label="",style="dashed", color="magenta", weight=3]; 2590[label="vuz42",fontsize=16,color="green",shape="box"];2591[label="vuz43",fontsize=16,color="green",shape="box"];2592[label="vuz42",fontsize=16,color="green",shape="box"];2593[label="vuz43",fontsize=16,color="green",shape="box"];2594[label="vuz42",fontsize=16,color="green",shape="box"];2595[label="vuz43",fontsize=16,color="green",shape="box"];2596[label="vuz42",fontsize=16,color="green",shape="box"];2597[label="vuz43",fontsize=16,color="green",shape="box"];4200 -> 4230[label="",style="dashed", color="red", weight=0]; 4200[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="magenta"];4200 -> 4231[label="",style="dashed", color="magenta", weight=3]; 4200 -> 4232[label="",style="dashed", color="magenta", weight=3]; 4201 -> 4233[label="",style="dashed", color="red", weight=0]; 4201[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="magenta"];4201 -> 4234[label="",style="dashed", color="magenta", weight=3]; 4201 -> 4235[label="",style="dashed", color="magenta", weight=3]; 2604[label="vuz47",fontsize=16,color="green",shape="box"];2605[label="vuz48",fontsize=16,color="green",shape="box"];2606[label="vuz47",fontsize=16,color="green",shape="box"];2607[label="vuz48",fontsize=16,color="green",shape="box"];2608[label="vuz47",fontsize=16,color="green",shape="box"];2609[label="vuz48",fontsize=16,color="green",shape="box"];2610[label="vuz47",fontsize=16,color="green",shape="box"];2611[label="vuz48",fontsize=16,color="green",shape="box"];4202 -> 4236[label="",style="dashed", color="red", weight=0]; 4202[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="magenta"];4202 -> 4237[label="",style="dashed", color="magenta", weight=3]; 4202 -> 4238[label="",style="dashed", color="magenta", weight=3]; 4203 -> 4239[label="",style="dashed", color="red", weight=0]; 4203[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="magenta"];4203 -> 4240[label="",style="dashed", color="magenta", weight=3]; 4203 -> 4241[label="",style="dashed", color="magenta", weight=3]; 2618[label="vuz52",fontsize=16,color="green",shape="box"];2619[label="vuz53",fontsize=16,color="green",shape="box"];2620[label="vuz52",fontsize=16,color="green",shape="box"];2621[label="vuz53",fontsize=16,color="green",shape="box"];2622[label="vuz52",fontsize=16,color="green",shape="box"];2623[label="vuz53",fontsize=16,color="green",shape="box"];2624[label="vuz52",fontsize=16,color="green",shape="box"];2625[label="vuz53",fontsize=16,color="green",shape="box"];5810 -> 5842[label="",style="dashed", color="red", weight=0]; 5810[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="magenta"];5810 -> 5843[label="",style="dashed", color="magenta", weight=3]; 5810 -> 5844[label="",style="dashed", color="magenta", weight=3]; 5811 -> 5845[label="",style="dashed", color="red", weight=0]; 5811[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="magenta"];5811 -> 5846[label="",style="dashed", color="magenta", weight=3]; 5811 -> 5847[label="",style="dashed", color="magenta", weight=3]; 2632[label="primQuotInt (primMinusNat (Succ vuz1850) vuz199) (reduce2D (primMinusNat (Succ vuz1850) vuz199) (Pos vuz144))",fontsize=16,color="burlywood",shape="box"];6528[label="vuz199/Succ vuz1990",fontsize=10,color="white",style="solid",shape="box"];2632 -> 6528[label="",style="solid", color="burlywood", weight=9]; 6528 -> 2734[label="",style="solid", color="burlywood", weight=3]; 6529[label="vuz199/Zero",fontsize=10,color="white",style="solid",shape="box"];2632 -> 6529[label="",style="solid", color="burlywood", weight=9]; 6529 -> 2735[label="",style="solid", color="burlywood", weight=3]; 2633[label="primQuotInt (primMinusNat Zero vuz199) (reduce2D (primMinusNat Zero vuz199) (Pos vuz144))",fontsize=16,color="burlywood",shape="box"];6530[label="vuz199/Succ vuz1990",fontsize=10,color="white",style="solid",shape="box"];2633 -> 6530[label="",style="solid", color="burlywood", weight=9]; 6530 -> 2736[label="",style="solid", color="burlywood", weight=3]; 6531[label="vuz199/Zero",fontsize=10,color="white",style="solid",shape="box"];2633 -> 6531[label="",style="solid", color="burlywood", weight=9]; 6531 -> 2737[label="",style="solid", color="burlywood", weight=3]; 3580 -> 4088[label="",style="dashed", color="red", weight=0]; 3580[label="reduce2D (Neg (primPlusNat vuz187 vuz201)) (Pos vuz144)",fontsize=16,color="magenta"];3580 -> 4089[label="",style="dashed", color="magenta", weight=3]; 3581 -> 1352[label="",style="dashed", color="red", weight=0]; 3581[label="primPlusNat vuz187 vuz201",fontsize=16,color="magenta"];3581 -> 4099[label="",style="dashed", color="magenta", weight=3]; 3581 -> 4100[label="",style="dashed", color="magenta", weight=3]; 5825 -> 678[label="",style="dashed", color="red", weight=0]; 5825[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];5825 -> 5848[label="",style="dashed", color="magenta", weight=3]; 5825 -> 5849[label="",style="dashed", color="magenta", weight=3]; 5826 -> 678[label="",style="dashed", color="red", weight=0]; 5826[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];5826 -> 5850[label="",style="dashed", color="magenta", weight=3]; 5826 -> 5851[label="",style="dashed", color="magenta", weight=3]; 5824[label="gcd2 (primEqInt (primPlusInt (Pos vuz350) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz349) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];5824 -> 5852[label="",style="solid", color="black", weight=3]; 5828 -> 678[label="",style="dashed", color="red", weight=0]; 5828[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];5828 -> 5853[label="",style="dashed", color="magenta", weight=3]; 5828 -> 5854[label="",style="dashed", color="magenta", weight=3]; 5829 -> 678[label="",style="dashed", color="red", weight=0]; 5829[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];5829 -> 5855[label="",style="dashed", color="magenta", weight=3]; 5829 -> 5856[label="",style="dashed", color="magenta", weight=3]; 5827[label="gcd2 (primEqInt (primPlusInt (Neg vuz352) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz351) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];5827 -> 5857[label="",style="solid", color="black", weight=3]; 3582 -> 4101[label="",style="dashed", color="red", weight=0]; 3582[label="reduce2D (Neg (primPlusNat vuz167 vuz203)) (Neg vuz68)",fontsize=16,color="magenta"];3582 -> 4102[label="",style="dashed", color="magenta", weight=3]; 3583 -> 1352[label="",style="dashed", color="red", weight=0]; 3583[label="primPlusNat vuz167 vuz203",fontsize=16,color="magenta"];3583 -> 4112[label="",style="dashed", color="magenta", weight=3]; 3583 -> 4113[label="",style="dashed", color="magenta", weight=3]; 2650[label="primQuotInt (primMinusNat (Succ vuz1690) vuz205) (reduce2D (primMinusNat (Succ vuz1690) vuz205) (Neg vuz68))",fontsize=16,color="burlywood",shape="box"];6532[label="vuz205/Succ vuz2050",fontsize=10,color="white",style="solid",shape="box"];2650 -> 6532[label="",style="solid", color="burlywood", weight=9]; 6532 -> 2750[label="",style="solid", color="burlywood", weight=3]; 6533[label="vuz205/Zero",fontsize=10,color="white",style="solid",shape="box"];2650 -> 6533[label="",style="solid", color="burlywood", weight=9]; 6533 -> 2751[label="",style="solid", color="burlywood", weight=3]; 2651[label="primQuotInt (primMinusNat Zero vuz205) (reduce2D (primMinusNat Zero vuz205) (Neg vuz68))",fontsize=16,color="burlywood",shape="box"];6534[label="vuz205/Succ vuz2050",fontsize=10,color="white",style="solid",shape="box"];2651 -> 6534[label="",style="solid", color="burlywood", weight=9]; 6534 -> 2752[label="",style="solid", color="burlywood", weight=3]; 6535[label="vuz205/Zero",fontsize=10,color="white",style="solid",shape="box"];2651 -> 6535[label="",style="solid", color="burlywood", weight=9]; 6535 -> 2753[label="",style="solid", color="burlywood", weight=3]; 4215 -> 678[label="",style="dashed", color="red", weight=0]; 4215[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];4215 -> 4242[label="",style="dashed", color="magenta", weight=3]; 4215 -> 4243[label="",style="dashed", color="magenta", weight=3]; 4216 -> 678[label="",style="dashed", color="red", weight=0]; 4216[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];4216 -> 4244[label="",style="dashed", color="magenta", weight=3]; 4216 -> 4245[label="",style="dashed", color="magenta", weight=3]; 4214[label="gcd2 (primEqInt (primPlusInt (Neg vuz285) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz284) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4214 -> 4246[label="",style="solid", color="black", weight=3]; 4218 -> 678[label="",style="dashed", color="red", weight=0]; 4218[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];4218 -> 4247[label="",style="dashed", color="magenta", weight=3]; 4218 -> 4248[label="",style="dashed", color="magenta", weight=3]; 4219 -> 678[label="",style="dashed", color="red", weight=0]; 4219[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];4219 -> 4249[label="",style="dashed", color="magenta", weight=3]; 4219 -> 4250[label="",style="dashed", color="magenta", weight=3]; 4217[label="gcd2 (primEqInt (primPlusInt (Pos vuz287) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz286) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4217 -> 4251[label="",style="solid", color="black", weight=3]; 4220 -> 4925[label="",style="dashed", color="red", weight=0]; 4220[label="primDivNatS0 (Succ vuz28000) (Succ vuz281000) (primGEqNatS vuz28000 vuz281000)",fontsize=16,color="magenta"];4220 -> 4926[label="",style="dashed", color="magenta", weight=3]; 4220 -> 4927[label="",style="dashed", color="magenta", weight=3]; 4220 -> 4928[label="",style="dashed", color="magenta", weight=3]; 4220 -> 4929[label="",style="dashed", color="magenta", weight=3]; 4221[label="primDivNatS0 (Succ vuz28000) Zero True",fontsize=16,color="black",shape="box"];4221 -> 4254[label="",style="solid", color="black", weight=3]; 4222[label="primDivNatS0 Zero (Succ vuz281000) False",fontsize=16,color="black",shape="box"];4222 -> 4255[label="",style="solid", color="black", weight=3]; 4223[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];4223 -> 4256[label="",style="solid", color="black", weight=3]; 5112 -> 1352[label="",style="dashed", color="red", weight=0]; 5112[label="primPlusNat vuz171 vuz207",fontsize=16,color="magenta"];5112 -> 5687[label="",style="dashed", color="magenta", weight=3]; 5112 -> 5688[label="",style="dashed", color="magenta", weight=3]; 5113 -> 5689[label="",style="dashed", color="red", weight=0]; 5113[label="reduce2D (Pos (primPlusNat vuz171 vuz207)) (Neg vuz71)",fontsize=16,color="magenta"];5113 -> 5690[label="",style="dashed", color="magenta", weight=3]; 2665[label="vuz173",fontsize=16,color="green",shape="box"];2666[label="vuz71",fontsize=16,color="green",shape="box"];2667[label="vuz209",fontsize=16,color="green",shape="box"];4225 -> 678[label="",style="dashed", color="red", weight=0]; 4225[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];4225 -> 4257[label="",style="dashed", color="magenta", weight=3]; 4225 -> 4258[label="",style="dashed", color="magenta", weight=3]; 4226 -> 678[label="",style="dashed", color="red", weight=0]; 4226[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];4226 -> 4259[label="",style="dashed", color="magenta", weight=3]; 4226 -> 4260[label="",style="dashed", color="magenta", weight=3]; 4224[label="gcd2 (primEqInt (primPlusInt (Pos vuz289) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz288) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4224 -> 4261[label="",style="solid", color="black", weight=3]; 4228 -> 678[label="",style="dashed", color="red", weight=0]; 4228[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];4228 -> 4262[label="",style="dashed", color="magenta", weight=3]; 4228 -> 4263[label="",style="dashed", color="magenta", weight=3]; 4229 -> 678[label="",style="dashed", color="red", weight=0]; 4229[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];4229 -> 4264[label="",style="dashed", color="magenta", weight=3]; 4229 -> 4265[label="",style="dashed", color="magenta", weight=3]; 4227[label="gcd2 (primEqInt (primPlusInt (Neg vuz291) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz290) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4227 -> 4266[label="",style="solid", color="black", weight=3]; 2678[label="vuz175",fontsize=16,color="green",shape="box"];2679[label="vuz74",fontsize=16,color="green",shape="box"];2680[label="vuz211",fontsize=16,color="green",shape="box"];5114 -> 1352[label="",style="dashed", color="red", weight=0]; 5114[label="primPlusNat vuz177 vuz213",fontsize=16,color="magenta"];5114 -> 5703[label="",style="dashed", color="magenta", weight=3]; 5114 -> 5704[label="",style="dashed", color="magenta", weight=3]; 5115 -> 5705[label="",style="dashed", color="red", weight=0]; 5115[label="reduce2D (Pos (primPlusNat vuz177 vuz213)) (Pos vuz74)",fontsize=16,color="magenta"];5115 -> 5706[label="",style="dashed", color="magenta", weight=3]; 5831 -> 678[label="",style="dashed", color="red", weight=0]; 5831[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];5831 -> 5858[label="",style="dashed", color="magenta", weight=3]; 5831 -> 5859[label="",style="dashed", color="magenta", weight=3]; 5832 -> 678[label="",style="dashed", color="red", weight=0]; 5832[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];5832 -> 5860[label="",style="dashed", color="magenta", weight=3]; 5832 -> 5861[label="",style="dashed", color="magenta", weight=3]; 5830[label="gcd2 (primEqInt (primPlusInt (Neg vuz354) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz353) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5830 -> 5862[label="",style="solid", color="black", weight=3]; 5834 -> 678[label="",style="dashed", color="red", weight=0]; 5834[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];5834 -> 5863[label="",style="dashed", color="magenta", weight=3]; 5834 -> 5864[label="",style="dashed", color="magenta", weight=3]; 5835 -> 678[label="",style="dashed", color="red", weight=0]; 5835[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];5835 -> 5865[label="",style="dashed", color="magenta", weight=3]; 5835 -> 5866[label="",style="dashed", color="magenta", weight=3]; 5833[label="gcd2 (primEqInt (primPlusInt (Pos vuz356) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz355) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5833 -> 5867[label="",style="solid", color="black", weight=3]; 5837 -> 678[label="",style="dashed", color="red", weight=0]; 5837[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];5837 -> 5868[label="",style="dashed", color="magenta", weight=3]; 5837 -> 5869[label="",style="dashed", color="magenta", weight=3]; 5838 -> 678[label="",style="dashed", color="red", weight=0]; 5838[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];5838 -> 5870[label="",style="dashed", color="magenta", weight=3]; 5838 -> 5871[label="",style="dashed", color="magenta", weight=3]; 5836[label="gcd2 (primEqInt (primPlusInt (Pos vuz358) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz357) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="triangle"];5836 -> 5872[label="",style="solid", color="black", weight=3]; 5840 -> 678[label="",style="dashed", color="red", weight=0]; 5840[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];5840 -> 5873[label="",style="dashed", color="magenta", weight=3]; 5840 -> 5874[label="",style="dashed", color="magenta", weight=3]; 5841 -> 678[label="",style="dashed", color="red", weight=0]; 5841[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];5841 -> 5875[label="",style="dashed", color="magenta", weight=3]; 5841 -> 5876[label="",style="dashed", color="magenta", weight=3]; 5839[label="gcd2 (primEqInt (primPlusInt (Neg vuz360) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz359) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="triangle"];5839 -> 5877[label="",style="solid", color="black", weight=3]; 4231 -> 678[label="",style="dashed", color="red", weight=0]; 4231[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];4231 -> 4267[label="",style="dashed", color="magenta", weight=3]; 4231 -> 4268[label="",style="dashed", color="magenta", weight=3]; 4232 -> 678[label="",style="dashed", color="red", weight=0]; 4232[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];4232 -> 4269[label="",style="dashed", color="magenta", weight=3]; 4232 -> 4270[label="",style="dashed", color="magenta", weight=3]; 4230[label="gcd2 (primEqInt (primPlusInt (Neg vuz293) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz292) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="triangle"];4230 -> 4271[label="",style="solid", color="black", weight=3]; 4234 -> 678[label="",style="dashed", color="red", weight=0]; 4234[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];4234 -> 4272[label="",style="dashed", color="magenta", weight=3]; 4234 -> 4273[label="",style="dashed", color="magenta", weight=3]; 4235 -> 678[label="",style="dashed", color="red", weight=0]; 4235[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];4235 -> 4274[label="",style="dashed", color="magenta", weight=3]; 4235 -> 4275[label="",style="dashed", color="magenta", weight=3]; 4233[label="gcd2 (primEqInt (primPlusInt (Pos vuz295) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz294) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="triangle"];4233 -> 4276[label="",style="solid", color="black", weight=3]; 4237 -> 678[label="",style="dashed", color="red", weight=0]; 4237[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];4237 -> 4277[label="",style="dashed", color="magenta", weight=3]; 4237 -> 4278[label="",style="dashed", color="magenta", weight=3]; 4238 -> 678[label="",style="dashed", color="red", weight=0]; 4238[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];4238 -> 4279[label="",style="dashed", color="magenta", weight=3]; 4238 -> 4280[label="",style="dashed", color="magenta", weight=3]; 4236[label="gcd2 (primEqInt (primPlusInt (Pos vuz297) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz296) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="triangle"];4236 -> 4281[label="",style="solid", color="black", weight=3]; 4240 -> 678[label="",style="dashed", color="red", weight=0]; 4240[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];4240 -> 4282[label="",style="dashed", color="magenta", weight=3]; 4240 -> 4283[label="",style="dashed", color="magenta", weight=3]; 4241 -> 678[label="",style="dashed", color="red", weight=0]; 4241[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];4241 -> 4284[label="",style="dashed", color="magenta", weight=3]; 4241 -> 4285[label="",style="dashed", color="magenta", weight=3]; 4239[label="gcd2 (primEqInt (primPlusInt (Neg vuz299) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz298) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="triangle"];4239 -> 4286[label="",style="solid", color="black", weight=3]; 5843 -> 678[label="",style="dashed", color="red", weight=0]; 5843[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];5843 -> 5878[label="",style="dashed", color="magenta", weight=3]; 5843 -> 5879[label="",style="dashed", color="magenta", weight=3]; 5844 -> 678[label="",style="dashed", color="red", weight=0]; 5844[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];5844 -> 5880[label="",style="dashed", color="magenta", weight=3]; 5844 -> 5881[label="",style="dashed", color="magenta", weight=3]; 5842[label="gcd2 (primEqInt (primPlusInt (Neg vuz362) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz361) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="triangle"];5842 -> 5882[label="",style="solid", color="black", weight=3]; 5846 -> 678[label="",style="dashed", color="red", weight=0]; 5846[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];5846 -> 5883[label="",style="dashed", color="magenta", weight=3]; 5846 -> 5884[label="",style="dashed", color="magenta", weight=3]; 5847 -> 678[label="",style="dashed", color="red", weight=0]; 5847[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];5847 -> 5885[label="",style="dashed", color="magenta", weight=3]; 5847 -> 5886[label="",style="dashed", color="magenta", weight=3]; 5845[label="gcd2 (primEqInt (primPlusInt (Pos vuz364) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz363) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="triangle"];5845 -> 5887[label="",style="solid", color="black", weight=3]; 2734[label="primQuotInt (primMinusNat (Succ vuz1850) (Succ vuz1990)) (reduce2D (primMinusNat (Succ vuz1850) (Succ vuz1990)) (Pos vuz144))",fontsize=16,color="black",shape="box"];2734 -> 2778[label="",style="solid", color="black", weight=3]; 2735[label="primQuotInt (primMinusNat (Succ vuz1850) Zero) (reduce2D (primMinusNat (Succ vuz1850) Zero) (Pos vuz144))",fontsize=16,color="black",shape="box"];2735 -> 2779[label="",style="solid", color="black", weight=3]; 2736[label="primQuotInt (primMinusNat Zero (Succ vuz1990)) (reduce2D (primMinusNat Zero (Succ vuz1990)) (Pos vuz144))",fontsize=16,color="black",shape="box"];2736 -> 2780[label="",style="solid", color="black", weight=3]; 2737[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero Zero) (Pos vuz144))",fontsize=16,color="black",shape="box"];2737 -> 2781[label="",style="solid", color="black", weight=3]; 4089 -> 1352[label="",style="dashed", color="red", weight=0]; 4089[label="primPlusNat vuz187 vuz201",fontsize=16,color="magenta"];4089 -> 4114[label="",style="dashed", color="magenta", weight=3]; 4089 -> 4115[label="",style="dashed", color="magenta", weight=3]; 4088[label="reduce2D (Neg vuz282) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];4088 -> 4116[label="",style="solid", color="black", weight=3]; 4099[label="vuz201",fontsize=16,color="green",shape="box"];4100[label="vuz187",fontsize=16,color="green",shape="box"];5848[label="vuz90",fontsize=16,color="green",shape="box"];5849[label="vuz10",fontsize=16,color="green",shape="box"];5850[label="vuz90",fontsize=16,color="green",shape="box"];5851[label="vuz10",fontsize=16,color="green",shape="box"];5852[label="gcd2 (primEqInt (primPlusInt (Pos vuz350) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz349) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5852 -> 5898[label="",style="solid", color="black", weight=3]; 5853[label="vuz90",fontsize=16,color="green",shape="box"];5854[label="vuz10",fontsize=16,color="green",shape="box"];5855[label="vuz90",fontsize=16,color="green",shape="box"];5856[label="vuz10",fontsize=16,color="green",shape="box"];5857[label="gcd2 (primEqInt (primPlusInt (Neg vuz352) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz351) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5857 -> 5899[label="",style="solid", color="black", weight=3]; 4102 -> 1352[label="",style="dashed", color="red", weight=0]; 4102[label="primPlusNat vuz167 vuz203",fontsize=16,color="magenta"];4102 -> 4117[label="",style="dashed", color="magenta", weight=3]; 4102 -> 4118[label="",style="dashed", color="magenta", weight=3]; 4101[label="reduce2D (Neg vuz283) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4101 -> 4119[label="",style="solid", color="black", weight=3]; 4112[label="vuz203",fontsize=16,color="green",shape="box"];4113[label="vuz167",fontsize=16,color="green",shape="box"];2750[label="primQuotInt (primMinusNat (Succ vuz1690) (Succ vuz2050)) (reduce2D (primMinusNat (Succ vuz1690) (Succ vuz2050)) (Neg vuz68))",fontsize=16,color="black",shape="box"];2750 -> 2802[label="",style="solid", color="black", weight=3]; 2751[label="primQuotInt (primMinusNat (Succ vuz1690) Zero) (reduce2D (primMinusNat (Succ vuz1690) Zero) (Neg vuz68))",fontsize=16,color="black",shape="box"];2751 -> 2803[label="",style="solid", color="black", weight=3]; 2752[label="primQuotInt (primMinusNat Zero (Succ vuz2050)) (reduce2D (primMinusNat Zero (Succ vuz2050)) (Neg vuz68))",fontsize=16,color="black",shape="box"];2752 -> 2804[label="",style="solid", color="black", weight=3]; 2753[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero Zero) (Neg vuz68))",fontsize=16,color="black",shape="box"];2753 -> 2805[label="",style="solid", color="black", weight=3]; 4242[label="vuz200",fontsize=16,color="green",shape="box"];4243[label="vuz21",fontsize=16,color="green",shape="box"];4244[label="vuz200",fontsize=16,color="green",shape="box"];4245[label="vuz21",fontsize=16,color="green",shape="box"];4246[label="gcd2 (primEqInt (primPlusInt (Neg vuz285) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz284) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4246 -> 4295[label="",style="solid", color="black", weight=3]; 4247[label="vuz200",fontsize=16,color="green",shape="box"];4248[label="vuz21",fontsize=16,color="green",shape="box"];4249[label="vuz200",fontsize=16,color="green",shape="box"];4250[label="vuz21",fontsize=16,color="green",shape="box"];4251[label="gcd2 (primEqInt (primPlusInt (Pos vuz287) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz286) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4251 -> 4296[label="",style="solid", color="black", weight=3]; 4926[label="vuz28000",fontsize=16,color="green",shape="box"];4927[label="vuz281000",fontsize=16,color="green",shape="box"];4928[label="vuz281000",fontsize=16,color="green",shape="box"];4929[label="vuz28000",fontsize=16,color="green",shape="box"];4925[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS vuz340 vuz341)",fontsize=16,color="burlywood",shape="triangle"];6536[label="vuz340/Succ vuz3400",fontsize=10,color="white",style="solid",shape="box"];4925 -> 6536[label="",style="solid", color="burlywood", weight=9]; 6536 -> 4966[label="",style="solid", color="burlywood", weight=3]; 6537[label="vuz340/Zero",fontsize=10,color="white",style="solid",shape="box"];4925 -> 6537[label="",style="solid", color="burlywood", weight=9]; 6537 -> 4967[label="",style="solid", color="burlywood", weight=3]; 4254[label="Succ (primDivNatS (primMinusNatS (Succ vuz28000) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];4254 -> 4301[label="",style="dashed", color="green", weight=3]; 4255[label="Zero",fontsize=16,color="green",shape="box"];4256[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];4256 -> 4302[label="",style="dashed", color="green", weight=3]; 5687[label="vuz207",fontsize=16,color="green",shape="box"];5688[label="vuz171",fontsize=16,color="green",shape="box"];5690 -> 1352[label="",style="dashed", color="red", weight=0]; 5690[label="primPlusNat vuz171 vuz207",fontsize=16,color="magenta"];5690 -> 5719[label="",style="dashed", color="magenta", weight=3]; 5690 -> 5720[label="",style="dashed", color="magenta", weight=3]; 5689[label="reduce2D (Pos vuz347) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];5689 -> 5721[label="",style="solid", color="black", weight=3]; 4257[label="vuz250",fontsize=16,color="green",shape="box"];4258[label="vuz26",fontsize=16,color="green",shape="box"];4259[label="vuz250",fontsize=16,color="green",shape="box"];4260[label="vuz26",fontsize=16,color="green",shape="box"];4261[label="gcd2 (primEqInt (primPlusInt (Pos vuz289) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz288) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4261 -> 4303[label="",style="solid", color="black", weight=3]; 4262[label="vuz250",fontsize=16,color="green",shape="box"];4263[label="vuz26",fontsize=16,color="green",shape="box"];4264[label="vuz250",fontsize=16,color="green",shape="box"];4265[label="vuz26",fontsize=16,color="green",shape="box"];4266[label="gcd2 (primEqInt (primPlusInt (Neg vuz291) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz290) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4266 -> 4304[label="",style="solid", color="black", weight=3]; 5703[label="vuz213",fontsize=16,color="green",shape="box"];5704[label="vuz177",fontsize=16,color="green",shape="box"];5706 -> 1352[label="",style="dashed", color="red", weight=0]; 5706[label="primPlusNat vuz177 vuz213",fontsize=16,color="magenta"];5706 -> 5722[label="",style="dashed", color="magenta", weight=3]; 5706 -> 5723[label="",style="dashed", color="magenta", weight=3]; 5705[label="reduce2D (Pos vuz348) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5705 -> 5724[label="",style="solid", color="black", weight=3]; 5858[label="vuz300",fontsize=16,color="green",shape="box"];5859[label="vuz31",fontsize=16,color="green",shape="box"];5860[label="vuz300",fontsize=16,color="green",shape="box"];5861[label="vuz31",fontsize=16,color="green",shape="box"];5862[label="gcd2 (primEqInt (primPlusInt (Neg vuz354) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz353) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5862 -> 5900[label="",style="solid", color="black", weight=3]; 5863[label="vuz300",fontsize=16,color="green",shape="box"];5864[label="vuz31",fontsize=16,color="green",shape="box"];5865[label="vuz300",fontsize=16,color="green",shape="box"];5866[label="vuz31",fontsize=16,color="green",shape="box"];5867[label="gcd2 (primEqInt (primPlusInt (Pos vuz356) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz355) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5867 -> 5901[label="",style="solid", color="black", weight=3]; 5868[label="vuz350",fontsize=16,color="green",shape="box"];5869[label="vuz36",fontsize=16,color="green",shape="box"];5870[label="vuz350",fontsize=16,color="green",shape="box"];5871[label="vuz36",fontsize=16,color="green",shape="box"];5872[label="gcd2 (primEqInt (primPlusInt (Pos vuz358) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz357) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5872 -> 5902[label="",style="solid", color="black", weight=3]; 5873[label="vuz350",fontsize=16,color="green",shape="box"];5874[label="vuz36",fontsize=16,color="green",shape="box"];5875[label="vuz350",fontsize=16,color="green",shape="box"];5876[label="vuz36",fontsize=16,color="green",shape="box"];5877[label="gcd2 (primEqInt (primPlusInt (Neg vuz360) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz359) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5877 -> 5903[label="",style="solid", color="black", weight=3]; 4267[label="vuz400",fontsize=16,color="green",shape="box"];4268[label="vuz41",fontsize=16,color="green",shape="box"];4269[label="vuz400",fontsize=16,color="green",shape="box"];4270[label="vuz41",fontsize=16,color="green",shape="box"];4271[label="gcd2 (primEqInt (primPlusInt (Neg vuz293) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz292) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4271 -> 4305[label="",style="solid", color="black", weight=3]; 4272[label="vuz400",fontsize=16,color="green",shape="box"];4273[label="vuz41",fontsize=16,color="green",shape="box"];4274[label="vuz400",fontsize=16,color="green",shape="box"];4275[label="vuz41",fontsize=16,color="green",shape="box"];4276[label="gcd2 (primEqInt (primPlusInt (Pos vuz295) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz294) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4276 -> 4306[label="",style="solid", color="black", weight=3]; 4277[label="vuz450",fontsize=16,color="green",shape="box"];4278[label="vuz46",fontsize=16,color="green",shape="box"];4279[label="vuz450",fontsize=16,color="green",shape="box"];4280[label="vuz46",fontsize=16,color="green",shape="box"];4281[label="gcd2 (primEqInt (primPlusInt (Pos vuz297) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz296) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4281 -> 4307[label="",style="solid", color="black", weight=3]; 4282[label="vuz450",fontsize=16,color="green",shape="box"];4283[label="vuz46",fontsize=16,color="green",shape="box"];4284[label="vuz450",fontsize=16,color="green",shape="box"];4285[label="vuz46",fontsize=16,color="green",shape="box"];4286[label="gcd2 (primEqInt (primPlusInt (Neg vuz299) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz298) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4286 -> 4308[label="",style="solid", color="black", weight=3]; 5878[label="vuz500",fontsize=16,color="green",shape="box"];5879[label="vuz51",fontsize=16,color="green",shape="box"];5880[label="vuz500",fontsize=16,color="green",shape="box"];5881[label="vuz51",fontsize=16,color="green",shape="box"];5882[label="gcd2 (primEqInt (primPlusInt (Neg vuz362) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz361) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5882 -> 5904[label="",style="solid", color="black", weight=3]; 5883[label="vuz500",fontsize=16,color="green",shape="box"];5884[label="vuz51",fontsize=16,color="green",shape="box"];5885[label="vuz500",fontsize=16,color="green",shape="box"];5886[label="vuz51",fontsize=16,color="green",shape="box"];5887[label="gcd2 (primEqInt (primPlusInt (Pos vuz364) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz363) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5887 -> 5905[label="",style="solid", color="black", weight=3]; 2778 -> 2516[label="",style="dashed", color="red", weight=0]; 2778[label="primQuotInt (primMinusNat vuz1850 vuz1990) (reduce2D (primMinusNat vuz1850 vuz1990) (Pos vuz144))",fontsize=16,color="magenta"];2778 -> 2862[label="",style="dashed", color="magenta", weight=3]; 2778 -> 2863[label="",style="dashed", color="magenta", weight=3]; 2779 -> 5044[label="",style="dashed", color="red", weight=0]; 2779[label="primQuotInt (Pos (Succ vuz1850)) (reduce2D (Pos (Succ vuz1850)) (Pos vuz144))",fontsize=16,color="magenta"];2779 -> 5162[label="",style="dashed", color="magenta", weight=3]; 2779 -> 5163[label="",style="dashed", color="magenta", weight=3]; 2780 -> 3507[label="",style="dashed", color="red", weight=0]; 2780[label="primQuotInt (Neg (Succ vuz1990)) (reduce2D (Neg (Succ vuz1990)) (Pos vuz144))",fontsize=16,color="magenta"];2780 -> 3640[label="",style="dashed", color="magenta", weight=3]; 2780 -> 3641[label="",style="dashed", color="magenta", weight=3]; 2781 -> 5044[label="",style="dashed", color="red", weight=0]; 2781[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos vuz144))",fontsize=16,color="magenta"];2781 -> 5164[label="",style="dashed", color="magenta", weight=3]; 2781 -> 5165[label="",style="dashed", color="magenta", weight=3]; 4114[label="vuz201",fontsize=16,color="green",shape="box"];4115[label="vuz187",fontsize=16,color="green",shape="box"];4116[label="gcd (Neg vuz282) (Pos vuz144)",fontsize=16,color="black",shape="box"];4116 -> 4133[label="",style="solid", color="black", weight=3]; 5898 -> 5918[label="",style="dashed", color="red", weight=0]; 5898[label="gcd2 (primEqInt (primPlusInt (Pos vuz350) (Neg (primMulNat vuz11 (Succ vuz12)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz349) (Neg (primMulNat vuz11 (Succ vuz12)))) (Pos vuz144)",fontsize=16,color="magenta"];5898 -> 5919[label="",style="dashed", color="magenta", weight=3]; 5898 -> 5920[label="",style="dashed", color="magenta", weight=3]; 5899 -> 5926[label="",style="dashed", color="red", weight=0]; 5899[label="gcd2 (primEqInt (primPlusInt (Neg vuz352) (Neg (primMulNat vuz11 (Succ vuz12)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz351) (Neg (primMulNat vuz11 (Succ vuz12)))) (Pos vuz144)",fontsize=16,color="magenta"];5899 -> 5927[label="",style="dashed", color="magenta", weight=3]; 5899 -> 5928[label="",style="dashed", color="magenta", weight=3]; 4117[label="vuz203",fontsize=16,color="green",shape="box"];4118[label="vuz167",fontsize=16,color="green",shape="box"];4119[label="gcd (Neg vuz283) (Neg vuz68)",fontsize=16,color="black",shape="box"];4119 -> 4134[label="",style="solid", color="black", weight=3]; 2802 -> 2537[label="",style="dashed", color="red", weight=0]; 2802[label="primQuotInt (primMinusNat vuz1690 vuz2050) (reduce2D (primMinusNat vuz1690 vuz2050) (Neg vuz68))",fontsize=16,color="magenta"];2802 -> 2884[label="",style="dashed", color="magenta", weight=3]; 2802 -> 2885[label="",style="dashed", color="magenta", weight=3]; 2803 -> 5044[label="",style="dashed", color="red", weight=0]; 2803[label="primQuotInt (Pos (Succ vuz1690)) (reduce2D (Pos (Succ vuz1690)) (Neg vuz68))",fontsize=16,color="magenta"];2803 -> 5170[label="",style="dashed", color="magenta", weight=3]; 2803 -> 5171[label="",style="dashed", color="magenta", weight=3]; 2804 -> 3507[label="",style="dashed", color="red", weight=0]; 2804[label="primQuotInt (Neg (Succ vuz2050)) (reduce2D (Neg (Succ vuz2050)) (Neg vuz68))",fontsize=16,color="magenta"];2804 -> 3646[label="",style="dashed", color="magenta", weight=3]; 2804 -> 3647[label="",style="dashed", color="magenta", weight=3]; 2805 -> 5044[label="",style="dashed", color="red", weight=0]; 2805[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg vuz68))",fontsize=16,color="magenta"];2805 -> 5172[label="",style="dashed", color="magenta", weight=3]; 2805 -> 5173[label="",style="dashed", color="magenta", weight=3]; 4295 -> 4317[label="",style="dashed", color="red", weight=0]; 4295[label="gcd2 (primEqInt (primPlusInt (Neg vuz285) (Neg (primMulNat vuz22 (Succ vuz23)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz284) (Neg (primMulNat vuz22 (Succ vuz23)))) (Neg vuz68)",fontsize=16,color="magenta"];4295 -> 4318[label="",style="dashed", color="magenta", weight=3]; 4295 -> 4319[label="",style="dashed", color="magenta", weight=3]; 4296 -> 4325[label="",style="dashed", color="red", weight=0]; 4296[label="gcd2 (primEqInt (primPlusInt (Pos vuz287) (Neg (primMulNat vuz22 (Succ vuz23)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz286) (Neg (primMulNat vuz22 (Succ vuz23)))) (Neg vuz68)",fontsize=16,color="magenta"];4296 -> 4326[label="",style="dashed", color="magenta", weight=3]; 4296 -> 4327[label="",style="dashed", color="magenta", weight=3]; 4966[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS (Succ vuz3400) vuz341)",fontsize=16,color="burlywood",shape="box"];6538[label="vuz341/Succ vuz3410",fontsize=10,color="white",style="solid",shape="box"];4966 -> 6538[label="",style="solid", color="burlywood", weight=9]; 6538 -> 4990[label="",style="solid", color="burlywood", weight=3]; 6539[label="vuz341/Zero",fontsize=10,color="white",style="solid",shape="box"];4966 -> 6539[label="",style="solid", color="burlywood", weight=9]; 6539 -> 4991[label="",style="solid", color="burlywood", weight=3]; 4967[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS Zero vuz341)",fontsize=16,color="burlywood",shape="box"];6540[label="vuz341/Succ vuz3410",fontsize=10,color="white",style="solid",shape="box"];4967 -> 6540[label="",style="solid", color="burlywood", weight=9]; 6540 -> 4992[label="",style="solid", color="burlywood", weight=3]; 6541[label="vuz341/Zero",fontsize=10,color="white",style="solid",shape="box"];4967 -> 6541[label="",style="solid", color="burlywood", weight=9]; 6541 -> 4993[label="",style="solid", color="burlywood", weight=3]; 4301 -> 4127[label="",style="dashed", color="red", weight=0]; 4301[label="primDivNatS (primMinusNatS (Succ vuz28000) Zero) (Succ Zero)",fontsize=16,color="magenta"];4301 -> 4337[label="",style="dashed", color="magenta", weight=3]; 4301 -> 4338[label="",style="dashed", color="magenta", weight=3]; 4302 -> 4127[label="",style="dashed", color="red", weight=0]; 4302[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];4302 -> 4339[label="",style="dashed", color="magenta", weight=3]; 4302 -> 4340[label="",style="dashed", color="magenta", weight=3]; 5719[label="vuz207",fontsize=16,color="green",shape="box"];5720[label="vuz171",fontsize=16,color="green",shape="box"];5721[label="gcd (Pos vuz347) (Neg vuz71)",fontsize=16,color="black",shape="box"];5721 -> 5739[label="",style="solid", color="black", weight=3]; 4303 -> 4341[label="",style="dashed", color="red", weight=0]; 4303[label="gcd2 (primEqInt (primPlusInt (Pos vuz289) (Pos (primMulNat vuz27 (Succ vuz28)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz288) (Pos (primMulNat vuz27 (Succ vuz28)))) (Neg vuz71)",fontsize=16,color="magenta"];4303 -> 4342[label="",style="dashed", color="magenta", weight=3]; 4303 -> 4343[label="",style="dashed", color="magenta", weight=3]; 4304 -> 4349[label="",style="dashed", color="red", weight=0]; 4304[label="gcd2 (primEqInt (primPlusInt (Neg vuz291) (Pos (primMulNat vuz27 (Succ vuz28)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz290) (Pos (primMulNat vuz27 (Succ vuz28)))) (Neg vuz71)",fontsize=16,color="magenta"];4304 -> 4350[label="",style="dashed", color="magenta", weight=3]; 4304 -> 4351[label="",style="dashed", color="magenta", weight=3]; 5722[label="vuz213",fontsize=16,color="green",shape="box"];5723[label="vuz177",fontsize=16,color="green",shape="box"];5724[label="gcd (Pos vuz348) (Pos vuz74)",fontsize=16,color="black",shape="box"];5724 -> 5740[label="",style="solid", color="black", weight=3]; 5900 -> 5934[label="",style="dashed", color="red", weight=0]; 5900[label="gcd2 (primEqInt (primPlusInt (Neg vuz354) (Pos (primMulNat vuz32 (Succ vuz33)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz353) (Pos (primMulNat vuz32 (Succ vuz33)))) (Pos vuz74)",fontsize=16,color="magenta"];5900 -> 5935[label="",style="dashed", color="magenta", weight=3]; 5900 -> 5936[label="",style="dashed", color="magenta", weight=3]; 5901 -> 5942[label="",style="dashed", color="red", weight=0]; 5901[label="gcd2 (primEqInt (primPlusInt (Pos vuz356) (Pos (primMulNat vuz32 (Succ vuz33)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz355) (Pos (primMulNat vuz32 (Succ vuz33)))) (Pos vuz74)",fontsize=16,color="magenta"];5901 -> 5943[label="",style="dashed", color="magenta", weight=3]; 5901 -> 5944[label="",style="dashed", color="magenta", weight=3]; 5902 -> 5942[label="",style="dashed", color="red", weight=0]; 5902[label="gcd2 (primEqInt (primPlusInt (Pos vuz358) (Pos (primMulNat vuz37 (Succ vuz38)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz357) (Pos (primMulNat vuz37 (Succ vuz38)))) (Pos vuz77)",fontsize=16,color="magenta"];5902 -> 5945[label="",style="dashed", color="magenta", weight=3]; 5902 -> 5946[label="",style="dashed", color="magenta", weight=3]; 5902 -> 5947[label="",style="dashed", color="magenta", weight=3]; 5902 -> 5948[label="",style="dashed", color="magenta", weight=3]; 5902 -> 5949[label="",style="dashed", color="magenta", weight=3]; 5903 -> 5934[label="",style="dashed", color="red", weight=0]; 5903[label="gcd2 (primEqInt (primPlusInt (Neg vuz360) (Pos (primMulNat vuz37 (Succ vuz38)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz359) (Pos (primMulNat vuz37 (Succ vuz38)))) (Pos vuz77)",fontsize=16,color="magenta"];5903 -> 5937[label="",style="dashed", color="magenta", weight=3]; 5903 -> 5938[label="",style="dashed", color="magenta", weight=3]; 5903 -> 5939[label="",style="dashed", color="magenta", weight=3]; 5903 -> 5940[label="",style="dashed", color="magenta", weight=3]; 5903 -> 5941[label="",style="dashed", color="magenta", weight=3]; 4305 -> 4349[label="",style="dashed", color="red", weight=0]; 4305[label="gcd2 (primEqInt (primPlusInt (Neg vuz293) (Pos (primMulNat vuz42 (Succ vuz43)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz292) (Pos (primMulNat vuz42 (Succ vuz43)))) (Neg vuz92)",fontsize=16,color="magenta"];4305 -> 4352[label="",style="dashed", color="magenta", weight=3]; 4305 -> 4353[label="",style="dashed", color="magenta", weight=3]; 4305 -> 4354[label="",style="dashed", color="magenta", weight=3]; 4305 -> 4355[label="",style="dashed", color="magenta", weight=3]; 4305 -> 4356[label="",style="dashed", color="magenta", weight=3]; 4306 -> 4341[label="",style="dashed", color="red", weight=0]; 4306[label="gcd2 (primEqInt (primPlusInt (Pos vuz295) (Pos (primMulNat vuz42 (Succ vuz43)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz294) (Pos (primMulNat vuz42 (Succ vuz43)))) (Neg vuz92)",fontsize=16,color="magenta"];4306 -> 4344[label="",style="dashed", color="magenta", weight=3]; 4306 -> 4345[label="",style="dashed", color="magenta", weight=3]; 4306 -> 4346[label="",style="dashed", color="magenta", weight=3]; 4306 -> 4347[label="",style="dashed", color="magenta", weight=3]; 4306 -> 4348[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4325[label="",style="dashed", color="red", weight=0]; 4307[label="gcd2 (primEqInt (primPlusInt (Pos vuz297) (Neg (primMulNat vuz47 (Succ vuz48)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz296) (Neg (primMulNat vuz47 (Succ vuz48)))) (Neg vuz107)",fontsize=16,color="magenta"];4307 -> 4328[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4329[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4330[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4331[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4332[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4317[label="",style="dashed", color="red", weight=0]; 4308[label="gcd2 (primEqInt (primPlusInt (Neg vuz299) (Neg (primMulNat vuz47 (Succ vuz48)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz298) (Neg (primMulNat vuz47 (Succ vuz48)))) (Neg vuz107)",fontsize=16,color="magenta"];4308 -> 4320[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4321[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4322[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4323[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4324[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5926[label="",style="dashed", color="red", weight=0]; 5904[label="gcd2 (primEqInt (primPlusInt (Neg vuz362) (Neg (primMulNat vuz52 (Succ vuz53)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz361) (Neg (primMulNat vuz52 (Succ vuz53)))) (Pos vuz122)",fontsize=16,color="magenta"];5904 -> 5929[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5930[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5931[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5932[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5933[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5918[label="",style="dashed", color="red", weight=0]; 5905[label="gcd2 (primEqInt (primPlusInt (Pos vuz364) (Neg (primMulNat vuz52 (Succ vuz53)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz363) (Neg (primMulNat vuz52 (Succ vuz53)))) (Pos vuz122)",fontsize=16,color="magenta"];5905 -> 5921[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5922[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5923[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5924[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5925[label="",style="dashed", color="magenta", weight=3]; 2862[label="vuz1990",fontsize=16,color="green",shape="box"];2863[label="vuz1850",fontsize=16,color="green",shape="box"];5162[label="Succ vuz1850",fontsize=16,color="green",shape="box"];5163 -> 5705[label="",style="dashed", color="red", weight=0]; 5163[label="reduce2D (Pos (Succ vuz1850)) (Pos vuz144)",fontsize=16,color="magenta"];5163 -> 5707[label="",style="dashed", color="magenta", weight=3]; 5163 -> 5708[label="",style="dashed", color="magenta", weight=3]; 3640 -> 4088[label="",style="dashed", color="red", weight=0]; 3640[label="reduce2D (Neg (Succ vuz1990)) (Pos vuz144)",fontsize=16,color="magenta"];3640 -> 4090[label="",style="dashed", color="magenta", weight=3]; 3641[label="Succ vuz1990",fontsize=16,color="green",shape="box"];5164[label="Zero",fontsize=16,color="green",shape="box"];5165 -> 5705[label="",style="dashed", color="red", weight=0]; 5165[label="reduce2D (Pos Zero) (Pos vuz144)",fontsize=16,color="magenta"];5165 -> 5709[label="",style="dashed", color="magenta", weight=3]; 5165 -> 5710[label="",style="dashed", color="magenta", weight=3]; 4133[label="gcd3 (Neg vuz282) (Pos vuz144)",fontsize=16,color="black",shape="box"];4133 -> 4149[label="",style="solid", color="black", weight=3]; 5919 -> 678[label="",style="dashed", color="red", weight=0]; 5919[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];5919 -> 5950[label="",style="dashed", color="magenta", weight=3]; 5919 -> 5951[label="",style="dashed", color="magenta", weight=3]; 5920 -> 678[label="",style="dashed", color="red", weight=0]; 5920[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];5920 -> 5952[label="",style="dashed", color="magenta", weight=3]; 5920 -> 5953[label="",style="dashed", color="magenta", weight=3]; 5918[label="gcd2 (primEqInt (primPlusInt (Pos vuz350) (Neg vuz366)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz349) (Neg vuz365)) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];5918 -> 5954[label="",style="solid", color="black", weight=3]; 5927 -> 678[label="",style="dashed", color="red", weight=0]; 5927[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];5927 -> 5955[label="",style="dashed", color="magenta", weight=3]; 5927 -> 5956[label="",style="dashed", color="magenta", weight=3]; 5928 -> 678[label="",style="dashed", color="red", weight=0]; 5928[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];5928 -> 5957[label="",style="dashed", color="magenta", weight=3]; 5928 -> 5958[label="",style="dashed", color="magenta", weight=3]; 5926[label="gcd2 (primEqInt (primPlusInt (Neg vuz352) (Neg vuz368)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz351) (Neg vuz367)) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];5926 -> 5959[label="",style="solid", color="black", weight=3]; 4134[label="gcd3 (Neg vuz283) (Neg vuz68)",fontsize=16,color="black",shape="box"];4134 -> 4150[label="",style="solid", color="black", weight=3]; 2884[label="vuz2050",fontsize=16,color="green",shape="box"];2885[label="vuz1690",fontsize=16,color="green",shape="box"];5170[label="Succ vuz1690",fontsize=16,color="green",shape="box"];5171 -> 5689[label="",style="dashed", color="red", weight=0]; 5171[label="reduce2D (Pos (Succ vuz1690)) (Neg vuz68)",fontsize=16,color="magenta"];5171 -> 5691[label="",style="dashed", color="magenta", weight=3]; 5171 -> 5692[label="",style="dashed", color="magenta", weight=3]; 3646 -> 4101[label="",style="dashed", color="red", weight=0]; 3646[label="reduce2D (Neg (Succ vuz2050)) (Neg vuz68)",fontsize=16,color="magenta"];3646 -> 4103[label="",style="dashed", color="magenta", weight=3]; 3647[label="Succ vuz2050",fontsize=16,color="green",shape="box"];5172[label="Zero",fontsize=16,color="green",shape="box"];5173 -> 5689[label="",style="dashed", color="red", weight=0]; 5173[label="reduce2D (Pos Zero) (Neg vuz68)",fontsize=16,color="magenta"];5173 -> 5693[label="",style="dashed", color="magenta", weight=3]; 5173 -> 5694[label="",style="dashed", color="magenta", weight=3]; 4318 -> 678[label="",style="dashed", color="red", weight=0]; 4318[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];4318 -> 4357[label="",style="dashed", color="magenta", weight=3]; 4318 -> 4358[label="",style="dashed", color="magenta", weight=3]; 4319 -> 678[label="",style="dashed", color="red", weight=0]; 4319[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];4319 -> 4359[label="",style="dashed", color="magenta", weight=3]; 4319 -> 4360[label="",style="dashed", color="magenta", weight=3]; 4317[label="gcd2 (primEqInt (primPlusInt (Neg vuz285) (Neg vuz301)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz284) (Neg vuz300)) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4317 -> 4361[label="",style="solid", color="black", weight=3]; 4326 -> 678[label="",style="dashed", color="red", weight=0]; 4326[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];4326 -> 4362[label="",style="dashed", color="magenta", weight=3]; 4326 -> 4363[label="",style="dashed", color="magenta", weight=3]; 4327 -> 678[label="",style="dashed", color="red", weight=0]; 4327[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];4327 -> 4364[label="",style="dashed", color="magenta", weight=3]; 4327 -> 4365[label="",style="dashed", color="magenta", weight=3]; 4325[label="gcd2 (primEqInt (primPlusInt (Pos vuz287) (Neg vuz303)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz286) (Neg vuz302)) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4325 -> 4366[label="",style="solid", color="black", weight=3]; 4990[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS (Succ vuz3400) (Succ vuz3410))",fontsize=16,color="black",shape="box"];4990 -> 5001[label="",style="solid", color="black", weight=3]; 4991[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS (Succ vuz3400) Zero)",fontsize=16,color="black",shape="box"];4991 -> 5002[label="",style="solid", color="black", weight=3]; 4992[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS Zero (Succ vuz3410))",fontsize=16,color="black",shape="box"];4992 -> 5003[label="",style="solid", color="black", weight=3]; 4993[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];4993 -> 5004[label="",style="solid", color="black", weight=3]; 4337[label="Zero",fontsize=16,color="green",shape="box"];4338[label="primMinusNatS (Succ vuz28000) Zero",fontsize=16,color="black",shape="triangle"];4338 -> 4372[label="",style="solid", color="black", weight=3]; 4339[label="Zero",fontsize=16,color="green",shape="box"];4340[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="triangle"];4340 -> 4373[label="",style="solid", color="black", weight=3]; 5739[label="gcd3 (Pos vuz347) (Neg vuz71)",fontsize=16,color="black",shape="box"];5739 -> 5756[label="",style="solid", color="black", weight=3]; 4342 -> 678[label="",style="dashed", color="red", weight=0]; 4342[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];4342 -> 4374[label="",style="dashed", color="magenta", weight=3]; 4342 -> 4375[label="",style="dashed", color="magenta", weight=3]; 4343 -> 678[label="",style="dashed", color="red", weight=0]; 4343[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];4343 -> 4376[label="",style="dashed", color="magenta", weight=3]; 4343 -> 4377[label="",style="dashed", color="magenta", weight=3]; 4341[label="gcd2 (primEqInt (primPlusInt (Pos vuz289) (Pos vuz305)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz288) (Pos vuz304)) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4341 -> 4378[label="",style="solid", color="black", weight=3]; 4350 -> 678[label="",style="dashed", color="red", weight=0]; 4350[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];4350 -> 4379[label="",style="dashed", color="magenta", weight=3]; 4350 -> 4380[label="",style="dashed", color="magenta", weight=3]; 4351 -> 678[label="",style="dashed", color="red", weight=0]; 4351[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];4351 -> 4381[label="",style="dashed", color="magenta", weight=3]; 4351 -> 4382[label="",style="dashed", color="magenta", weight=3]; 4349[label="gcd2 (primEqInt (primPlusInt (Neg vuz291) (Pos vuz307)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz290) (Pos vuz306)) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4349 -> 4383[label="",style="solid", color="black", weight=3]; 5740[label="gcd3 (Pos vuz348) (Pos vuz74)",fontsize=16,color="black",shape="box"];5740 -> 5757[label="",style="solid", color="black", weight=3]; 5935 -> 678[label="",style="dashed", color="red", weight=0]; 5935[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];5935 -> 5960[label="",style="dashed", color="magenta", weight=3]; 5935 -> 5961[label="",style="dashed", color="magenta", weight=3]; 5936 -> 678[label="",style="dashed", color="red", weight=0]; 5936[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];5936 -> 5962[label="",style="dashed", color="magenta", weight=3]; 5936 -> 5963[label="",style="dashed", color="magenta", weight=3]; 5934[label="gcd2 (primEqInt (primPlusInt (Neg vuz354) (Pos vuz370)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz353) (Pos vuz369)) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5934 -> 5964[label="",style="solid", color="black", weight=3]; 5943 -> 678[label="",style="dashed", color="red", weight=0]; 5943[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];5943 -> 5965[label="",style="dashed", color="magenta", weight=3]; 5943 -> 5966[label="",style="dashed", color="magenta", weight=3]; 5944 -> 678[label="",style="dashed", color="red", weight=0]; 5944[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];5944 -> 5967[label="",style="dashed", color="magenta", weight=3]; 5944 -> 5968[label="",style="dashed", color="magenta", weight=3]; 5942[label="gcd2 (primEqInt (primPlusInt (Pos vuz356) (Pos vuz372)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz355) (Pos vuz371)) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5942 -> 5969[label="",style="solid", color="black", weight=3]; 5945[label="vuz357",fontsize=16,color="green",shape="box"];5946[label="vuz358",fontsize=16,color="green",shape="box"];5947 -> 678[label="",style="dashed", color="red", weight=0]; 5947[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];5947 -> 5970[label="",style="dashed", color="magenta", weight=3]; 5947 -> 5971[label="",style="dashed", color="magenta", weight=3]; 5948[label="vuz77",fontsize=16,color="green",shape="box"];5949 -> 678[label="",style="dashed", color="red", weight=0]; 5949[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];5949 -> 5972[label="",style="dashed", color="magenta", weight=3]; 5949 -> 5973[label="",style="dashed", color="magenta", weight=3]; 5937[label="vuz77",fontsize=16,color="green",shape="box"];5938[label="vuz360",fontsize=16,color="green",shape="box"];5939 -> 678[label="",style="dashed", color="red", weight=0]; 5939[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];5939 -> 5974[label="",style="dashed", color="magenta", weight=3]; 5939 -> 5975[label="",style="dashed", color="magenta", weight=3]; 5940[label="vuz359",fontsize=16,color="green",shape="box"];5941 -> 678[label="",style="dashed", color="red", weight=0]; 5941[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];5941 -> 5976[label="",style="dashed", color="magenta", weight=3]; 5941 -> 5977[label="",style="dashed", color="magenta", weight=3]; 4352[label="vuz292",fontsize=16,color="green",shape="box"];4353 -> 678[label="",style="dashed", color="red", weight=0]; 4353[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];4353 -> 4384[label="",style="dashed", color="magenta", weight=3]; 4353 -> 4385[label="",style="dashed", color="magenta", weight=3]; 4354[label="vuz92",fontsize=16,color="green",shape="box"];4355[label="vuz293",fontsize=16,color="green",shape="box"];4356 -> 678[label="",style="dashed", color="red", weight=0]; 4356[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];4356 -> 4386[label="",style="dashed", color="magenta", weight=3]; 4356 -> 4387[label="",style="dashed", color="magenta", weight=3]; 4344[label="vuz295",fontsize=16,color="green",shape="box"];4345[label="vuz92",fontsize=16,color="green",shape="box"];4346[label="vuz294",fontsize=16,color="green",shape="box"];4347 -> 678[label="",style="dashed", color="red", weight=0]; 4347[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];4347 -> 4388[label="",style="dashed", color="magenta", weight=3]; 4347 -> 4389[label="",style="dashed", color="magenta", weight=3]; 4348 -> 678[label="",style="dashed", color="red", weight=0]; 4348[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];4348 -> 4390[label="",style="dashed", color="magenta", weight=3]; 4348 -> 4391[label="",style="dashed", color="magenta", weight=3]; 4328[label="vuz296",fontsize=16,color="green",shape="box"];4329 -> 678[label="",style="dashed", color="red", weight=0]; 4329[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];4329 -> 4392[label="",style="dashed", color="magenta", weight=3]; 4329 -> 4393[label="",style="dashed", color="magenta", weight=3]; 4330[label="vuz297",fontsize=16,color="green",shape="box"];4331 -> 678[label="",style="dashed", color="red", weight=0]; 4331[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];4331 -> 4394[label="",style="dashed", color="magenta", weight=3]; 4331 -> 4395[label="",style="dashed", color="magenta", weight=3]; 4332[label="vuz107",fontsize=16,color="green",shape="box"];4320 -> 678[label="",style="dashed", color="red", weight=0]; 4320[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];4320 -> 4396[label="",style="dashed", color="magenta", weight=3]; 4320 -> 4397[label="",style="dashed", color="magenta", weight=3]; 4321[label="vuz299",fontsize=16,color="green",shape="box"];4322[label="vuz107",fontsize=16,color="green",shape="box"];4323[label="vuz298",fontsize=16,color="green",shape="box"];4324 -> 678[label="",style="dashed", color="red", weight=0]; 4324[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];4324 -> 4398[label="",style="dashed", color="magenta", weight=3]; 4324 -> 4399[label="",style="dashed", color="magenta", weight=3]; 5929 -> 678[label="",style="dashed", color="red", weight=0]; 5929[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];5929 -> 5978[label="",style="dashed", color="magenta", weight=3]; 5929 -> 5979[label="",style="dashed", color="magenta", weight=3]; 5930[label="vuz361",fontsize=16,color="green",shape="box"];5931[label="vuz122",fontsize=16,color="green",shape="box"];5932[label="vuz362",fontsize=16,color="green",shape="box"];5933 -> 678[label="",style="dashed", color="red", weight=0]; 5933[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];5933 -> 5980[label="",style="dashed", color="magenta", weight=3]; 5933 -> 5981[label="",style="dashed", color="magenta", weight=3]; 5921 -> 678[label="",style="dashed", color="red", weight=0]; 5921[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];5921 -> 5982[label="",style="dashed", color="magenta", weight=3]; 5921 -> 5983[label="",style="dashed", color="magenta", weight=3]; 5922[label="vuz363",fontsize=16,color="green",shape="box"];5923 -> 678[label="",style="dashed", color="red", weight=0]; 5923[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];5923 -> 5984[label="",style="dashed", color="magenta", weight=3]; 5923 -> 5985[label="",style="dashed", color="magenta", weight=3]; 5924[label="vuz122",fontsize=16,color="green",shape="box"];5925[label="vuz364",fontsize=16,color="green",shape="box"];5707[label="vuz144",fontsize=16,color="green",shape="box"];5708[label="Succ vuz1850",fontsize=16,color="green",shape="box"];4090[label="Succ vuz1990",fontsize=16,color="green",shape="box"];5709[label="vuz144",fontsize=16,color="green",shape="box"];5710[label="Zero",fontsize=16,color="green",shape="box"];4149[label="gcd2 (Neg vuz282 == fromInt (Pos Zero)) (Neg vuz282) (Pos vuz144)",fontsize=16,color="black",shape="box"];4149 -> 4164[label="",style="solid", color="black", weight=3]; 5950[label="vuz11",fontsize=16,color="green",shape="box"];5951[label="vuz12",fontsize=16,color="green",shape="box"];5952[label="vuz11",fontsize=16,color="green",shape="box"];5953[label="vuz12",fontsize=16,color="green",shape="box"];5954[label="gcd2 (primEqInt (primMinusNat vuz350 vuz366) (fromInt (Pos Zero))) (primMinusNat vuz350 vuz366) (Pos vuz144)",fontsize=16,color="burlywood",shape="triangle"];6542[label="vuz350/Succ vuz3500",fontsize=10,color="white",style="solid",shape="box"];5954 -> 6542[label="",style="solid", color="burlywood", weight=9]; 6542 -> 6002[label="",style="solid", color="burlywood", weight=3]; 6543[label="vuz350/Zero",fontsize=10,color="white",style="solid",shape="box"];5954 -> 6543[label="",style="solid", color="burlywood", weight=9]; 6543 -> 6003[label="",style="solid", color="burlywood", weight=3]; 5955[label="vuz11",fontsize=16,color="green",shape="box"];5956[label="vuz12",fontsize=16,color="green",shape="box"];5957[label="vuz11",fontsize=16,color="green",shape="box"];5958[label="vuz12",fontsize=16,color="green",shape="box"];5959 -> 4164[label="",style="dashed", color="red", weight=0]; 5959[label="gcd2 (primEqInt (Neg (primPlusNat vuz352 vuz368)) (fromInt (Pos Zero))) (Neg (primPlusNat vuz352 vuz368)) (Pos vuz144)",fontsize=16,color="magenta"];5959 -> 6004[label="",style="dashed", color="magenta", weight=3]; 4150[label="gcd2 (Neg vuz283 == fromInt (Pos Zero)) (Neg vuz283) (Neg vuz68)",fontsize=16,color="black",shape="box"];4150 -> 4165[label="",style="solid", color="black", weight=3]; 5691[label="vuz68",fontsize=16,color="green",shape="box"];5692[label="Succ vuz1690",fontsize=16,color="green",shape="box"];4103[label="Succ vuz2050",fontsize=16,color="green",shape="box"];5693[label="vuz68",fontsize=16,color="green",shape="box"];5694[label="Zero",fontsize=16,color="green",shape="box"];4357[label="vuz22",fontsize=16,color="green",shape="box"];4358[label="vuz23",fontsize=16,color="green",shape="box"];4359[label="vuz22",fontsize=16,color="green",shape="box"];4360[label="vuz23",fontsize=16,color="green",shape="box"];4361 -> 4165[label="",style="dashed", color="red", weight=0]; 4361[label="gcd2 (primEqInt (Neg (primPlusNat vuz285 vuz301)) (fromInt (Pos Zero))) (Neg (primPlusNat vuz285 vuz301)) (Neg vuz68)",fontsize=16,color="magenta"];4361 -> 4408[label="",style="dashed", color="magenta", weight=3]; 4362[label="vuz22",fontsize=16,color="green",shape="box"];4363[label="vuz23",fontsize=16,color="green",shape="box"];4364[label="vuz22",fontsize=16,color="green",shape="box"];4365[label="vuz23",fontsize=16,color="green",shape="box"];4366[label="gcd2 (primEqInt (primMinusNat vuz287 vuz303) (fromInt (Pos Zero))) (primMinusNat vuz287 vuz303) (Neg vuz68)",fontsize=16,color="burlywood",shape="triangle"];6544[label="vuz287/Succ vuz2870",fontsize=10,color="white",style="solid",shape="box"];4366 -> 6544[label="",style="solid", color="burlywood", weight=9]; 6544 -> 4409[label="",style="solid", color="burlywood", weight=3]; 6545[label="vuz287/Zero",fontsize=10,color="white",style="solid",shape="box"];4366 -> 6545[label="",style="solid", color="burlywood", weight=9]; 6545 -> 4410[label="",style="solid", color="burlywood", weight=3]; 5001 -> 4925[label="",style="dashed", color="red", weight=0]; 5001[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS vuz3400 vuz3410)",fontsize=16,color="magenta"];5001 -> 5011[label="",style="dashed", color="magenta", weight=3]; 5001 -> 5012[label="",style="dashed", color="magenta", weight=3]; 5002[label="primDivNatS0 (Succ vuz338) (Succ vuz339) True",fontsize=16,color="black",shape="triangle"];5002 -> 5013[label="",style="solid", color="black", weight=3]; 5003[label="primDivNatS0 (Succ vuz338) (Succ vuz339) False",fontsize=16,color="black",shape="box"];5003 -> 5014[label="",style="solid", color="black", weight=3]; 5004 -> 5002[label="",style="dashed", color="red", weight=0]; 5004[label="primDivNatS0 (Succ vuz338) (Succ vuz339) True",fontsize=16,color="magenta"];4372[label="Succ vuz28000",fontsize=16,color="green",shape="box"];4373[label="Zero",fontsize=16,color="green",shape="box"];5756[label="gcd2 (Pos vuz347 == fromInt (Pos Zero)) (Pos vuz347) (Neg vuz71)",fontsize=16,color="black",shape="box"];5756 -> 5771[label="",style="solid", color="black", weight=3]; 4374[label="vuz27",fontsize=16,color="green",shape="box"];4375[label="vuz28",fontsize=16,color="green",shape="box"];4376[label="vuz27",fontsize=16,color="green",shape="box"];4377[label="vuz28",fontsize=16,color="green",shape="box"];4378 -> 4417[label="",style="dashed", color="red", weight=0]; 4378[label="gcd2 (primEqInt (Pos (primPlusNat vuz289 vuz305)) (fromInt (Pos Zero))) (Pos (primPlusNat vuz289 vuz305)) (Neg vuz71)",fontsize=16,color="magenta"];4378 -> 4418[label="",style="dashed", color="magenta", weight=3]; 4378 -> 4419[label="",style="dashed", color="magenta", weight=3]; 4379[label="vuz27",fontsize=16,color="green",shape="box"];4380[label="vuz28",fontsize=16,color="green",shape="box"];4381[label="vuz27",fontsize=16,color="green",shape="box"];4382[label="vuz28",fontsize=16,color="green",shape="box"];4383 -> 4366[label="",style="dashed", color="red", weight=0]; 4383[label="gcd2 (primEqInt (primMinusNat vuz307 vuz291) (fromInt (Pos Zero))) (primMinusNat vuz307 vuz291) (Neg vuz71)",fontsize=16,color="magenta"];4383 -> 4420[label="",style="dashed", color="magenta", weight=3]; 4383 -> 4421[label="",style="dashed", color="magenta", weight=3]; 4383 -> 4422[label="",style="dashed", color="magenta", weight=3]; 5757[label="gcd2 (Pos vuz348 == fromInt (Pos Zero)) (Pos vuz348) (Pos vuz74)",fontsize=16,color="black",shape="box"];5757 -> 5772[label="",style="solid", color="black", weight=3]; 5960[label="vuz32",fontsize=16,color="green",shape="box"];5961[label="vuz33",fontsize=16,color="green",shape="box"];5962[label="vuz32",fontsize=16,color="green",shape="box"];5963[label="vuz33",fontsize=16,color="green",shape="box"];5964 -> 5954[label="",style="dashed", color="red", weight=0]; 5964[label="gcd2 (primEqInt (primMinusNat vuz370 vuz354) (fromInt (Pos Zero))) (primMinusNat vuz370 vuz354) (Pos vuz74)",fontsize=16,color="magenta"];5964 -> 6005[label="",style="dashed", color="magenta", weight=3]; 5964 -> 6006[label="",style="dashed", color="magenta", weight=3]; 5964 -> 6007[label="",style="dashed", color="magenta", weight=3]; 5965[label="vuz32",fontsize=16,color="green",shape="box"];5966[label="vuz33",fontsize=16,color="green",shape="box"];5967[label="vuz32",fontsize=16,color="green",shape="box"];5968[label="vuz33",fontsize=16,color="green",shape="box"];5969 -> 5772[label="",style="dashed", color="red", weight=0]; 5969[label="gcd2 (primEqInt (Pos (primPlusNat vuz356 vuz372)) (fromInt (Pos Zero))) (Pos (primPlusNat vuz356 vuz372)) (Pos vuz74)",fontsize=16,color="magenta"];5969 -> 6008[label="",style="dashed", color="magenta", weight=3]; 5970[label="vuz37",fontsize=16,color="green",shape="box"];5971[label="vuz38",fontsize=16,color="green",shape="box"];5972[label="vuz37",fontsize=16,color="green",shape="box"];5973[label="vuz38",fontsize=16,color="green",shape="box"];5974[label="vuz37",fontsize=16,color="green",shape="box"];5975[label="vuz38",fontsize=16,color="green",shape="box"];5976[label="vuz37",fontsize=16,color="green",shape="box"];5977[label="vuz38",fontsize=16,color="green",shape="box"];4384[label="vuz42",fontsize=16,color="green",shape="box"];4385[label="vuz43",fontsize=16,color="green",shape="box"];4386[label="vuz42",fontsize=16,color="green",shape="box"];4387[label="vuz43",fontsize=16,color="green",shape="box"];4388[label="vuz42",fontsize=16,color="green",shape="box"];4389[label="vuz43",fontsize=16,color="green",shape="box"];4390[label="vuz42",fontsize=16,color="green",shape="box"];4391[label="vuz43",fontsize=16,color="green",shape="box"];4392[label="vuz47",fontsize=16,color="green",shape="box"];4393[label="vuz48",fontsize=16,color="green",shape="box"];4394[label="vuz47",fontsize=16,color="green",shape="box"];4395[label="vuz48",fontsize=16,color="green",shape="box"];4396[label="vuz47",fontsize=16,color="green",shape="box"];4397[label="vuz48",fontsize=16,color="green",shape="box"];4398[label="vuz47",fontsize=16,color="green",shape="box"];4399[label="vuz48",fontsize=16,color="green",shape="box"];5978[label="vuz52",fontsize=16,color="green",shape="box"];5979[label="vuz53",fontsize=16,color="green",shape="box"];5980[label="vuz52",fontsize=16,color="green",shape="box"];5981[label="vuz53",fontsize=16,color="green",shape="box"];5982[label="vuz52",fontsize=16,color="green",shape="box"];5983[label="vuz53",fontsize=16,color="green",shape="box"];5984[label="vuz52",fontsize=16,color="green",shape="box"];5985[label="vuz53",fontsize=16,color="green",shape="box"];4164[label="gcd2 (primEqInt (Neg vuz282) (fromInt (Pos Zero))) (Neg vuz282) (Pos vuz144)",fontsize=16,color="burlywood",shape="triangle"];6546[label="vuz282/Succ vuz2820",fontsize=10,color="white",style="solid",shape="box"];4164 -> 6546[label="",style="solid", color="burlywood", weight=9]; 6546 -> 4183[label="",style="solid", color="burlywood", weight=3]; 6547[label="vuz282/Zero",fontsize=10,color="white",style="solid",shape="box"];4164 -> 6547[label="",style="solid", color="burlywood", weight=9]; 6547 -> 4184[label="",style="solid", color="burlywood", weight=3]; 6002[label="gcd2 (primEqInt (primMinusNat (Succ vuz3500) vuz366) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3500) vuz366) (Pos vuz144)",fontsize=16,color="burlywood",shape="box"];6548[label="vuz366/Succ vuz3660",fontsize=10,color="white",style="solid",shape="box"];6002 -> 6548[label="",style="solid", color="burlywood", weight=9]; 6548 -> 6024[label="",style="solid", color="burlywood", weight=3]; 6549[label="vuz366/Zero",fontsize=10,color="white",style="solid",shape="box"];6002 -> 6549[label="",style="solid", color="burlywood", weight=9]; 6549 -> 6025[label="",style="solid", color="burlywood", weight=3]; 6003[label="gcd2 (primEqInt (primMinusNat Zero vuz366) (fromInt (Pos Zero))) (primMinusNat Zero vuz366) (Pos vuz144)",fontsize=16,color="burlywood",shape="box"];6550[label="vuz366/Succ vuz3660",fontsize=10,color="white",style="solid",shape="box"];6003 -> 6550[label="",style="solid", color="burlywood", weight=9]; 6550 -> 6026[label="",style="solid", color="burlywood", weight=3]; 6551[label="vuz366/Zero",fontsize=10,color="white",style="solid",shape="box"];6003 -> 6551[label="",style="solid", color="burlywood", weight=9]; 6551 -> 6027[label="",style="solid", color="burlywood", weight=3]; 6004 -> 1352[label="",style="dashed", color="red", weight=0]; 6004[label="primPlusNat vuz352 vuz368",fontsize=16,color="magenta"];6004 -> 6028[label="",style="dashed", color="magenta", weight=3]; 6004 -> 6029[label="",style="dashed", color="magenta", weight=3]; 4165[label="gcd2 (primEqInt (Neg vuz283) (fromInt (Pos Zero))) (Neg vuz283) (Neg vuz68)",fontsize=16,color="burlywood",shape="triangle"];6552[label="vuz283/Succ vuz2830",fontsize=10,color="white",style="solid",shape="box"];4165 -> 6552[label="",style="solid", color="burlywood", weight=9]; 6552 -> 4185[label="",style="solid", color="burlywood", weight=3]; 6553[label="vuz283/Zero",fontsize=10,color="white",style="solid",shape="box"];4165 -> 6553[label="",style="solid", color="burlywood", weight=9]; 6553 -> 4186[label="",style="solid", color="burlywood", weight=3]; 4408 -> 1352[label="",style="dashed", color="red", weight=0]; 4408[label="primPlusNat vuz285 vuz301",fontsize=16,color="magenta"];4408 -> 4423[label="",style="dashed", color="magenta", weight=3]; 4408 -> 4424[label="",style="dashed", color="magenta", weight=3]; 4409[label="gcd2 (primEqInt (primMinusNat (Succ vuz2870) vuz303) (fromInt (Pos Zero))) (primMinusNat (Succ vuz2870) vuz303) (Neg vuz68)",fontsize=16,color="burlywood",shape="box"];6554[label="vuz303/Succ vuz3030",fontsize=10,color="white",style="solid",shape="box"];4409 -> 6554[label="",style="solid", color="burlywood", weight=9]; 6554 -> 4425[label="",style="solid", color="burlywood", weight=3]; 6555[label="vuz303/Zero",fontsize=10,color="white",style="solid",shape="box"];4409 -> 6555[label="",style="solid", color="burlywood", weight=9]; 6555 -> 4426[label="",style="solid", color="burlywood", weight=3]; 4410[label="gcd2 (primEqInt (primMinusNat Zero vuz303) (fromInt (Pos Zero))) (primMinusNat Zero vuz303) (Neg vuz68)",fontsize=16,color="burlywood",shape="box"];6556[label="vuz303/Succ vuz3030",fontsize=10,color="white",style="solid",shape="box"];4410 -> 6556[label="",style="solid", color="burlywood", weight=9]; 6556 -> 4427[label="",style="solid", color="burlywood", weight=3]; 6557[label="vuz303/Zero",fontsize=10,color="white",style="solid",shape="box"];4410 -> 6557[label="",style="solid", color="burlywood", weight=9]; 6557 -> 4428[label="",style="solid", color="burlywood", weight=3]; 5011[label="vuz3410",fontsize=16,color="green",shape="box"];5012[label="vuz3400",fontsize=16,color="green",shape="box"];5013[label="Succ (primDivNatS (primMinusNatS (Succ vuz338) (Succ vuz339)) (Succ (Succ vuz339)))",fontsize=16,color="green",shape="box"];5013 -> 5037[label="",style="dashed", color="green", weight=3]; 5014[label="Zero",fontsize=16,color="green",shape="box"];5771 -> 4417[label="",style="dashed", color="red", weight=0]; 5771[label="gcd2 (primEqInt (Pos vuz347) (fromInt (Pos Zero))) (Pos vuz347) (Neg vuz71)",fontsize=16,color="magenta"];5771 -> 5790[label="",style="dashed", color="magenta", weight=3]; 5771 -> 5791[label="",style="dashed", color="magenta", weight=3]; 4418 -> 1352[label="",style="dashed", color="red", weight=0]; 4418[label="primPlusNat vuz289 vuz305",fontsize=16,color="magenta"];4418 -> 4437[label="",style="dashed", color="magenta", weight=3]; 4418 -> 4438[label="",style="dashed", color="magenta", weight=3]; 4419 -> 1352[label="",style="dashed", color="red", weight=0]; 4419[label="primPlusNat vuz289 vuz305",fontsize=16,color="magenta"];4419 -> 4439[label="",style="dashed", color="magenta", weight=3]; 4419 -> 4440[label="",style="dashed", color="magenta", weight=3]; 4417[label="gcd2 (primEqInt (Pos vuz309) (fromInt (Pos Zero))) (Pos vuz308) (Neg vuz71)",fontsize=16,color="burlywood",shape="triangle"];6558[label="vuz309/Succ vuz3090",fontsize=10,color="white",style="solid",shape="box"];4417 -> 6558[label="",style="solid", color="burlywood", weight=9]; 6558 -> 4441[label="",style="solid", color="burlywood", weight=3]; 6559[label="vuz309/Zero",fontsize=10,color="white",style="solid",shape="box"];4417 -> 6559[label="",style="solid", color="burlywood", weight=9]; 6559 -> 4442[label="",style="solid", color="burlywood", weight=3]; 4420[label="vuz291",fontsize=16,color="green",shape="box"];4421[label="vuz307",fontsize=16,color="green",shape="box"];4422[label="vuz71",fontsize=16,color="green",shape="box"];5772[label="gcd2 (primEqInt (Pos vuz348) (fromInt (Pos Zero))) (Pos vuz348) (Pos vuz74)",fontsize=16,color="burlywood",shape="triangle"];6560[label="vuz348/Succ vuz3480",fontsize=10,color="white",style="solid",shape="box"];5772 -> 6560[label="",style="solid", color="burlywood", weight=9]; 6560 -> 5792[label="",style="solid", color="burlywood", weight=3]; 6561[label="vuz348/Zero",fontsize=10,color="white",style="solid",shape="box"];5772 -> 6561[label="",style="solid", color="burlywood", weight=9]; 6561 -> 5793[label="",style="solid", color="burlywood", weight=3]; 6005[label="vuz354",fontsize=16,color="green",shape="box"];6006[label="vuz74",fontsize=16,color="green",shape="box"];6007[label="vuz370",fontsize=16,color="green",shape="box"];6008 -> 1352[label="",style="dashed", color="red", weight=0]; 6008[label="primPlusNat vuz356 vuz372",fontsize=16,color="magenta"];6008 -> 6030[label="",style="dashed", color="magenta", weight=3]; 6008 -> 6031[label="",style="dashed", color="magenta", weight=3]; 4183[label="gcd2 (primEqInt (Neg (Succ vuz2820)) (fromInt (Pos Zero))) (Neg (Succ vuz2820)) (Pos vuz144)",fontsize=16,color="black",shape="box"];4183 -> 4204[label="",style="solid", color="black", weight=3]; 4184[label="gcd2 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];4184 -> 4205[label="",style="solid", color="black", weight=3]; 6024[label="gcd2 (primEqInt (primMinusNat (Succ vuz3500) (Succ vuz3660)) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3500) (Succ vuz3660)) (Pos vuz144)",fontsize=16,color="black",shape="box"];6024 -> 6047[label="",style="solid", color="black", weight=3]; 6025[label="gcd2 (primEqInt (primMinusNat (Succ vuz3500) Zero) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3500) Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];6025 -> 6048[label="",style="solid", color="black", weight=3]; 6026[label="gcd2 (primEqInt (primMinusNat Zero (Succ vuz3660)) (fromInt (Pos Zero))) (primMinusNat Zero (Succ vuz3660)) (Pos vuz144)",fontsize=16,color="black",shape="box"];6026 -> 6049[label="",style="solid", color="black", weight=3]; 6027[label="gcd2 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (primMinusNat Zero Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];6027 -> 6050[label="",style="solid", color="black", weight=3]; 6028[label="vuz368",fontsize=16,color="green",shape="box"];6029[label="vuz352",fontsize=16,color="green",shape="box"];4185[label="gcd2 (primEqInt (Neg (Succ vuz2830)) (fromInt (Pos Zero))) (Neg (Succ vuz2830)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4185 -> 4206[label="",style="solid", color="black", weight=3]; 4186[label="gcd2 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4186 -> 4207[label="",style="solid", color="black", weight=3]; 4423[label="vuz301",fontsize=16,color="green",shape="box"];4424[label="vuz285",fontsize=16,color="green",shape="box"];4425[label="gcd2 (primEqInt (primMinusNat (Succ vuz2870) (Succ vuz3030)) (fromInt (Pos Zero))) (primMinusNat (Succ vuz2870) (Succ vuz3030)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4425 -> 4453[label="",style="solid", color="black", weight=3]; 4426[label="gcd2 (primEqInt (primMinusNat (Succ vuz2870) Zero) (fromInt (Pos Zero))) (primMinusNat (Succ vuz2870) Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4426 -> 4454[label="",style="solid", color="black", weight=3]; 4427[label="gcd2 (primEqInt (primMinusNat Zero (Succ vuz3030)) (fromInt (Pos Zero))) (primMinusNat Zero (Succ vuz3030)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4427 -> 4455[label="",style="solid", color="black", weight=3]; 4428[label="gcd2 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (primMinusNat Zero Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4428 -> 4456[label="",style="solid", color="black", weight=3]; 5037 -> 4127[label="",style="dashed", color="red", weight=0]; 5037[label="primDivNatS (primMinusNatS (Succ vuz338) (Succ vuz339)) (Succ (Succ vuz339))",fontsize=16,color="magenta"];5037 -> 5725[label="",style="dashed", color="magenta", weight=3]; 5037 -> 5726[label="",style="dashed", color="magenta", weight=3]; 5790[label="vuz347",fontsize=16,color="green",shape="box"];5791[label="vuz347",fontsize=16,color="green",shape="box"];4437[label="vuz305",fontsize=16,color="green",shape="box"];4438[label="vuz289",fontsize=16,color="green",shape="box"];4439[label="vuz305",fontsize=16,color="green",shape="box"];4440[label="vuz289",fontsize=16,color="green",shape="box"];4441[label="gcd2 (primEqInt (Pos (Succ vuz3090)) (fromInt (Pos Zero))) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4441 -> 4464[label="",style="solid", color="black", weight=3]; 4442[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4442 -> 4465[label="",style="solid", color="black", weight=3]; 5792[label="gcd2 (primEqInt (Pos (Succ vuz3480)) (fromInt (Pos Zero))) (Pos (Succ vuz3480)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5792 -> 5812[label="",style="solid", color="black", weight=3]; 5793[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz74)",fontsize=16,color="black",shape="box"];5793 -> 5813[label="",style="solid", color="black", weight=3]; 6030[label="vuz372",fontsize=16,color="green",shape="box"];6031[label="vuz356",fontsize=16,color="green",shape="box"];4204[label="gcd2 (primEqInt (Neg (Succ vuz2820)) (Pos Zero)) (Neg (Succ vuz2820)) (Pos vuz144)",fontsize=16,color="black",shape="box"];4204 -> 4287[label="",style="solid", color="black", weight=3]; 4205[label="gcd2 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];4205 -> 4288[label="",style="solid", color="black", weight=3]; 6047 -> 5954[label="",style="dashed", color="red", weight=0]; 6047[label="gcd2 (primEqInt (primMinusNat vuz3500 vuz3660) (fromInt (Pos Zero))) (primMinusNat vuz3500 vuz3660) (Pos vuz144)",fontsize=16,color="magenta"];6047 -> 6057[label="",style="dashed", color="magenta", weight=3]; 6047 -> 6058[label="",style="dashed", color="magenta", weight=3]; 6048 -> 5772[label="",style="dashed", color="red", weight=0]; 6048[label="gcd2 (primEqInt (Pos (Succ vuz3500)) (fromInt (Pos Zero))) (Pos (Succ vuz3500)) (Pos vuz144)",fontsize=16,color="magenta"];6048 -> 6059[label="",style="dashed", color="magenta", weight=3]; 6048 -> 6060[label="",style="dashed", color="magenta", weight=3]; 6049 -> 4164[label="",style="dashed", color="red", weight=0]; 6049[label="gcd2 (primEqInt (Neg (Succ vuz3660)) (fromInt (Pos Zero))) (Neg (Succ vuz3660)) (Pos vuz144)",fontsize=16,color="magenta"];6049 -> 6061[label="",style="dashed", color="magenta", weight=3]; 6050 -> 5772[label="",style="dashed", color="red", weight=0]; 6050[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz144)",fontsize=16,color="magenta"];6050 -> 6062[label="",style="dashed", color="magenta", weight=3]; 6050 -> 6063[label="",style="dashed", color="magenta", weight=3]; 4206[label="gcd2 (primEqInt (Neg (Succ vuz2830)) (Pos Zero)) (Neg (Succ vuz2830)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4206 -> 4289[label="",style="solid", color="black", weight=3]; 4207[label="gcd2 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4207 -> 4290[label="",style="solid", color="black", weight=3]; 4453 -> 4366[label="",style="dashed", color="red", weight=0]; 4453[label="gcd2 (primEqInt (primMinusNat vuz2870 vuz3030) (fromInt (Pos Zero))) (primMinusNat vuz2870 vuz3030) (Neg vuz68)",fontsize=16,color="magenta"];4453 -> 4476[label="",style="dashed", color="magenta", weight=3]; 4453 -> 4477[label="",style="dashed", color="magenta", weight=3]; 4454 -> 4417[label="",style="dashed", color="red", weight=0]; 4454[label="gcd2 (primEqInt (Pos (Succ vuz2870)) (fromInt (Pos Zero))) (Pos (Succ vuz2870)) (Neg vuz68)",fontsize=16,color="magenta"];4454 -> 4478[label="",style="dashed", color="magenta", weight=3]; 4454 -> 4479[label="",style="dashed", color="magenta", weight=3]; 4454 -> 4480[label="",style="dashed", color="magenta", weight=3]; 4455 -> 4165[label="",style="dashed", color="red", weight=0]; 4455[label="gcd2 (primEqInt (Neg (Succ vuz3030)) (fromInt (Pos Zero))) (Neg (Succ vuz3030)) (Neg vuz68)",fontsize=16,color="magenta"];4455 -> 4481[label="",style="dashed", color="magenta", weight=3]; 4456 -> 4417[label="",style="dashed", color="red", weight=0]; 4456[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Neg vuz68)",fontsize=16,color="magenta"];4456 -> 4482[label="",style="dashed", color="magenta", weight=3]; 4456 -> 4483[label="",style="dashed", color="magenta", weight=3]; 4456 -> 4484[label="",style="dashed", color="magenta", weight=3]; 5725[label="Succ vuz339",fontsize=16,color="green",shape="box"];5726[label="primMinusNatS (Succ vuz338) (Succ vuz339)",fontsize=16,color="black",shape="box"];5726 -> 5741[label="",style="solid", color="black", weight=3]; 4464[label="gcd2 (primEqInt (Pos (Succ vuz3090)) (Pos Zero)) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4464 -> 4492[label="",style="solid", color="black", weight=3]; 4465[label="gcd2 (primEqInt (Pos Zero) (Pos Zero)) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4465 -> 4493[label="",style="solid", color="black", weight=3]; 5812[label="gcd2 (primEqInt (Pos (Succ vuz3480)) (Pos Zero)) (Pos (Succ vuz3480)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5812 -> 5888[label="",style="solid", color="black", weight=3]; 5813[label="gcd2 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (Pos vuz74)",fontsize=16,color="black",shape="box"];5813 -> 5889[label="",style="solid", color="black", weight=3]; 4287[label="gcd2 False (Neg (Succ vuz2820)) (Pos vuz144)",fontsize=16,color="black",shape="box"];4287 -> 4309[label="",style="solid", color="black", weight=3]; 4288[label="gcd2 True (Neg Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];4288 -> 4310[label="",style="solid", color="black", weight=3]; 6057[label="vuz3660",fontsize=16,color="green",shape="box"];6058[label="vuz3500",fontsize=16,color="green",shape="box"];6059[label="vuz144",fontsize=16,color="green",shape="box"];6060[label="Succ vuz3500",fontsize=16,color="green",shape="box"];6061[label="Succ vuz3660",fontsize=16,color="green",shape="box"];6062[label="vuz144",fontsize=16,color="green",shape="box"];6063[label="Zero",fontsize=16,color="green",shape="box"];4289[label="gcd2 False (Neg (Succ vuz2830)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4289 -> 4311[label="",style="solid", color="black", weight=3]; 4290[label="gcd2 True (Neg Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4290 -> 4312[label="",style="solid", color="black", weight=3]; 4476[label="vuz3030",fontsize=16,color="green",shape="box"];4477[label="vuz2870",fontsize=16,color="green",shape="box"];4478[label="Succ vuz2870",fontsize=16,color="green",shape="box"];4479[label="Succ vuz2870",fontsize=16,color="green",shape="box"];4480[label="vuz68",fontsize=16,color="green",shape="box"];4481[label="Succ vuz3030",fontsize=16,color="green",shape="box"];4482[label="Zero",fontsize=16,color="green",shape="box"];4483[label="Zero",fontsize=16,color="green",shape="box"];4484[label="vuz68",fontsize=16,color="green",shape="box"];5741[label="primMinusNatS vuz338 vuz339",fontsize=16,color="burlywood",shape="triangle"];6562[label="vuz338/Succ vuz3380",fontsize=10,color="white",style="solid",shape="box"];5741 -> 6562[label="",style="solid", color="burlywood", weight=9]; 6562 -> 5758[label="",style="solid", color="burlywood", weight=3]; 6563[label="vuz338/Zero",fontsize=10,color="white",style="solid",shape="box"];5741 -> 6563[label="",style="solid", color="burlywood", weight=9]; 6563 -> 5759[label="",style="solid", color="burlywood", weight=3]; 4492[label="gcd2 False (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4492 -> 4515[label="",style="solid", color="black", weight=3]; 4493[label="gcd2 True (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4493 -> 4516[label="",style="solid", color="black", weight=3]; 5888[label="gcd2 False (Pos (Succ vuz3480)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5888 -> 5906[label="",style="solid", color="black", weight=3]; 5889[label="gcd2 True (Pos Zero) (Pos vuz74)",fontsize=16,color="black",shape="box"];5889 -> 5907[label="",style="solid", color="black", weight=3]; 4309[label="gcd0 (Neg (Succ vuz2820)) (Pos vuz144)",fontsize=16,color="black",shape="box"];4309 -> 4400[label="",style="solid", color="black", weight=3]; 4310[label="gcd1 (Pos vuz144 == fromInt (Pos Zero)) (Neg Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];4310 -> 4401[label="",style="solid", color="black", weight=3]; 4311[label="gcd0 (Neg (Succ vuz2830)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4311 -> 4402[label="",style="solid", color="black", weight=3]; 4312[label="gcd1 (Neg vuz68 == fromInt (Pos Zero)) (Neg Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4312 -> 4403[label="",style="solid", color="black", weight=3]; 5758[label="primMinusNatS (Succ vuz3380) vuz339",fontsize=16,color="burlywood",shape="box"];6564[label="vuz339/Succ vuz3390",fontsize=10,color="white",style="solid",shape="box"];5758 -> 6564[label="",style="solid", color="burlywood", weight=9]; 6564 -> 5773[label="",style="solid", color="burlywood", weight=3]; 6565[label="vuz339/Zero",fontsize=10,color="white",style="solid",shape="box"];5758 -> 6565[label="",style="solid", color="burlywood", weight=9]; 6565 -> 5774[label="",style="solid", color="burlywood", weight=3]; 5759[label="primMinusNatS Zero vuz339",fontsize=16,color="burlywood",shape="box"];6566[label="vuz339/Succ vuz3390",fontsize=10,color="white",style="solid",shape="box"];5759 -> 6566[label="",style="solid", color="burlywood", weight=9]; 6566 -> 5775[label="",style="solid", color="burlywood", weight=3]; 6567[label="vuz339/Zero",fontsize=10,color="white",style="solid",shape="box"];5759 -> 6567[label="",style="solid", color="burlywood", weight=9]; 6567 -> 5776[label="",style="solid", color="burlywood", weight=3]; 4515[label="gcd0 (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4515 -> 4537[label="",style="solid", color="black", weight=3]; 4516[label="gcd1 (Neg vuz71 == fromInt (Pos Zero)) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4516 -> 4538[label="",style="solid", color="black", weight=3]; 5906[label="gcd0 (Pos (Succ vuz3480)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5906 -> 5986[label="",style="solid", color="black", weight=3]; 5907[label="gcd1 (Pos vuz74 == fromInt (Pos Zero)) (Pos Zero) (Pos vuz74)",fontsize=16,color="black",shape="box"];5907 -> 5987[label="",style="solid", color="black", weight=3]; 4400 -> 6009[label="",style="dashed", color="red", weight=0]; 4400[label="gcd0Gcd' (abs (Neg (Succ vuz2820))) (abs (Pos vuz144))",fontsize=16,color="magenta"];4400 -> 6010[label="",style="dashed", color="magenta", weight=3]; 4400 -> 6011[label="",style="dashed", color="magenta", weight=3]; 4401[label="gcd1 (primEqInt (Pos vuz144) (fromInt (Pos Zero))) (Neg Zero) (Pos vuz144)",fontsize=16,color="burlywood",shape="box"];6568[label="vuz144/Succ vuz1440",fontsize=10,color="white",style="solid",shape="box"];4401 -> 6568[label="",style="solid", color="burlywood", weight=9]; 6568 -> 4444[label="",style="solid", color="burlywood", weight=3]; 6569[label="vuz144/Zero",fontsize=10,color="white",style="solid",shape="box"];4401 -> 6569[label="",style="solid", color="burlywood", weight=9]; 6569 -> 4445[label="",style="solid", color="burlywood", weight=3]; 4402 -> 6009[label="",style="dashed", color="red", weight=0]; 4402[label="gcd0Gcd' (abs (Neg (Succ vuz2830))) (abs (Neg vuz68))",fontsize=16,color="magenta"];4402 -> 6012[label="",style="dashed", color="magenta", weight=3]; 4402 -> 6013[label="",style="dashed", color="magenta", weight=3]; 4403[label="gcd1 (primEqInt (Neg vuz68) (fromInt (Pos Zero))) (Neg Zero) (Neg vuz68)",fontsize=16,color="burlywood",shape="box"];6570[label="vuz68/Succ vuz680",fontsize=10,color="white",style="solid",shape="box"];4403 -> 6570[label="",style="solid", color="burlywood", weight=9]; 6570 -> 4447[label="",style="solid", color="burlywood", weight=3]; 6571[label="vuz68/Zero",fontsize=10,color="white",style="solid",shape="box"];4403 -> 6571[label="",style="solid", color="burlywood", weight=9]; 6571 -> 4448[label="",style="solid", color="burlywood", weight=3]; 5773[label="primMinusNatS (Succ vuz3380) (Succ vuz3390)",fontsize=16,color="black",shape="box"];5773 -> 5794[label="",style="solid", color="black", weight=3]; 5774[label="primMinusNatS (Succ vuz3380) Zero",fontsize=16,color="black",shape="box"];5774 -> 5795[label="",style="solid", color="black", weight=3]; 5775[label="primMinusNatS Zero (Succ vuz3390)",fontsize=16,color="black",shape="box"];5775 -> 5796[label="",style="solid", color="black", weight=3]; 5776[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="box"];5776 -> 5797[label="",style="solid", color="black", weight=3]; 4537 -> 6009[label="",style="dashed", color="red", weight=0]; 4537[label="gcd0Gcd' (abs (Pos vuz308)) (abs (Neg vuz71))",fontsize=16,color="magenta"];4537 -> 6014[label="",style="dashed", color="magenta", weight=3]; 4537 -> 6015[label="",style="dashed", color="magenta", weight=3]; 4538[label="gcd1 (primEqInt (Neg vuz71) (fromInt (Pos Zero))) (Pos vuz308) (Neg vuz71)",fontsize=16,color="burlywood",shape="box"];6572[label="vuz71/Succ vuz710",fontsize=10,color="white",style="solid",shape="box"];4538 -> 6572[label="",style="solid", color="burlywood", weight=9]; 6572 -> 4557[label="",style="solid", color="burlywood", weight=3]; 6573[label="vuz71/Zero",fontsize=10,color="white",style="solid",shape="box"];4538 -> 6573[label="",style="solid", color="burlywood", weight=9]; 6573 -> 4558[label="",style="solid", color="burlywood", weight=3]; 5986 -> 6009[label="",style="dashed", color="red", weight=0]; 5986[label="gcd0Gcd' (abs (Pos (Succ vuz3480))) (abs (Pos vuz74))",fontsize=16,color="magenta"];5986 -> 6016[label="",style="dashed", color="magenta", weight=3]; 5986 -> 6017[label="",style="dashed", color="magenta", weight=3]; 5987[label="gcd1 (primEqInt (Pos vuz74) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz74)",fontsize=16,color="burlywood",shape="box"];6574[label="vuz74/Succ vuz740",fontsize=10,color="white",style="solid",shape="box"];5987 -> 6574[label="",style="solid", color="burlywood", weight=9]; 6574 -> 6032[label="",style="solid", color="burlywood", weight=3]; 6575[label="vuz74/Zero",fontsize=10,color="white",style="solid",shape="box"];5987 -> 6575[label="",style="solid", color="burlywood", weight=9]; 6575 -> 6033[label="",style="solid", color="burlywood", weight=3]; 6010[label="abs (Neg (Succ vuz2820))",fontsize=16,color="black",shape="triangle"];6010 -> 6034[label="",style="solid", color="black", weight=3]; 6011[label="abs (Pos vuz144)",fontsize=16,color="black",shape="triangle"];6011 -> 6035[label="",style="solid", color="black", weight=3]; 6009[label="gcd0Gcd' vuz374 vuz373",fontsize=16,color="black",shape="triangle"];6009 -> 6036[label="",style="solid", color="black", weight=3]; 4444[label="gcd1 (primEqInt (Pos (Succ vuz1440)) (fromInt (Pos Zero))) (Neg Zero) (Pos (Succ vuz1440))",fontsize=16,color="black",shape="box"];4444 -> 4467[label="",style="solid", color="black", weight=3]; 4445[label="gcd1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];4445 -> 4468[label="",style="solid", color="black", weight=3]; 6012 -> 6010[label="",style="dashed", color="red", weight=0]; 6012[label="abs (Neg (Succ vuz2830))",fontsize=16,color="magenta"];6012 -> 6037[label="",style="dashed", color="magenta", weight=3]; 6013[label="abs (Neg vuz68)",fontsize=16,color="black",shape="triangle"];6013 -> 6038[label="",style="solid", color="black", weight=3]; 4447[label="gcd1 (primEqInt (Neg (Succ vuz680)) (fromInt (Pos Zero))) (Neg Zero) (Neg (Succ vuz680))",fontsize=16,color="black",shape="box"];4447 -> 4470[label="",style="solid", color="black", weight=3]; 4448[label="gcd1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];4448 -> 4471[label="",style="solid", color="black", weight=3]; 5794 -> 5741[label="",style="dashed", color="red", weight=0]; 5794[label="primMinusNatS vuz3380 vuz3390",fontsize=16,color="magenta"];5794 -> 5814[label="",style="dashed", color="magenta", weight=3]; 5794 -> 5815[label="",style="dashed", color="magenta", weight=3]; 5795[label="Succ vuz3380",fontsize=16,color="green",shape="box"];5796[label="Zero",fontsize=16,color="green",shape="box"];5797[label="Zero",fontsize=16,color="green",shape="box"];6014 -> 6011[label="",style="dashed", color="red", weight=0]; 6014[label="abs (Pos vuz308)",fontsize=16,color="magenta"];6014 -> 6039[label="",style="dashed", color="magenta", weight=3]; 6015 -> 6013[label="",style="dashed", color="red", weight=0]; 6015[label="abs (Neg vuz71)",fontsize=16,color="magenta"];6015 -> 6040[label="",style="dashed", color="magenta", weight=3]; 4557[label="gcd1 (primEqInt (Neg (Succ vuz710)) (fromInt (Pos Zero))) (Pos vuz308) (Neg (Succ vuz710))",fontsize=16,color="black",shape="box"];4557 -> 4577[label="",style="solid", color="black", weight=3]; 4558[label="gcd1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Pos vuz308) (Neg Zero)",fontsize=16,color="black",shape="box"];4558 -> 4578[label="",style="solid", color="black", weight=3]; 6016 -> 6011[label="",style="dashed", color="red", weight=0]; 6016[label="abs (Pos (Succ vuz3480))",fontsize=16,color="magenta"];6016 -> 6041[label="",style="dashed", color="magenta", weight=3]; 6017 -> 6011[label="",style="dashed", color="red", weight=0]; 6017[label="abs (Pos vuz74)",fontsize=16,color="magenta"];6017 -> 6042[label="",style="dashed", color="magenta", weight=3]; 6032[label="gcd1 (primEqInt (Pos (Succ vuz740)) (fromInt (Pos Zero))) (Pos Zero) (Pos (Succ vuz740))",fontsize=16,color="black",shape="box"];6032 -> 6051[label="",style="solid", color="black", weight=3]; 6033[label="gcd1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];6033 -> 6052[label="",style="solid", color="black", weight=3]; 6034[label="absReal (Neg (Succ vuz2820))",fontsize=16,color="black",shape="box"];6034 -> 6053[label="",style="solid", color="black", weight=3]; 6035[label="absReal (Pos vuz144)",fontsize=16,color="black",shape="box"];6035 -> 6054[label="",style="solid", color="black", weight=3]; 6036[label="gcd0Gcd'2 vuz374 vuz373",fontsize=16,color="black",shape="box"];6036 -> 6055[label="",style="solid", color="black", weight=3]; 4467[label="gcd1 (primEqInt (Pos (Succ vuz1440)) (Pos Zero)) (Neg Zero) (Pos (Succ vuz1440))",fontsize=16,color="black",shape="box"];4467 -> 4495[label="",style="solid", color="black", weight=3]; 4468[label="gcd1 (primEqInt (Pos Zero) (Pos Zero)) (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];4468 -> 4496[label="",style="solid", color="black", weight=3]; 6037[label="vuz2830",fontsize=16,color="green",shape="box"];6038[label="absReal (Neg vuz68)",fontsize=16,color="black",shape="box"];6038 -> 6056[label="",style="solid", color="black", weight=3]; 4470[label="gcd1 (primEqInt (Neg (Succ vuz680)) (Pos Zero)) (Neg Zero) (Neg (Succ vuz680))",fontsize=16,color="black",shape="box"];4470 -> 4498[label="",style="solid", color="black", weight=3]; 4471[label="gcd1 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];4471 -> 4499[label="",style="solid", color="black", weight=3]; 5814[label="vuz3380",fontsize=16,color="green",shape="box"];5815[label="vuz3390",fontsize=16,color="green",shape="box"];6039[label="vuz308",fontsize=16,color="green",shape="box"];6040[label="vuz71",fontsize=16,color="green",shape="box"];4577[label="gcd1 (primEqInt (Neg (Succ vuz710)) (Pos Zero)) (Pos vuz308) (Neg (Succ vuz710))",fontsize=16,color="black",shape="box"];4577 -> 4600[label="",style="solid", color="black", weight=3]; 4578[label="gcd1 (primEqInt (Neg Zero) (Pos Zero)) (Pos vuz308) (Neg Zero)",fontsize=16,color="black",shape="box"];4578 -> 4601[label="",style="solid", color="black", weight=3]; 6041[label="Succ vuz3480",fontsize=16,color="green",shape="box"];6042[label="vuz74",fontsize=16,color="green",shape="box"];6051[label="gcd1 (primEqInt (Pos (Succ vuz740)) (Pos Zero)) (Pos Zero) (Pos (Succ vuz740))",fontsize=16,color="black",shape="box"];6051 -> 6064[label="",style="solid", color="black", weight=3]; 6052[label="gcd1 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];6052 -> 6065[label="",style="solid", color="black", weight=3]; 6053[label="absReal2 (Neg (Succ vuz2820))",fontsize=16,color="black",shape="box"];6053 -> 6066[label="",style="solid", color="black", weight=3]; 6054[label="absReal2 (Pos vuz144)",fontsize=16,color="black",shape="box"];6054 -> 6067[label="",style="solid", color="black", weight=3]; 6055[label="gcd0Gcd'1 (vuz373 == fromInt (Pos Zero)) vuz374 vuz373",fontsize=16,color="black",shape="box"];6055 -> 6068[label="",style="solid", color="black", weight=3]; 4495[label="gcd1 False (Neg Zero) (Pos (Succ vuz1440))",fontsize=16,color="black",shape="box"];4495 -> 4518[label="",style="solid", color="black", weight=3]; 4496[label="gcd1 True (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];4496 -> 4519[label="",style="solid", color="black", weight=3]; 6056[label="absReal2 (Neg vuz68)",fontsize=16,color="black",shape="box"];6056 -> 6069[label="",style="solid", color="black", weight=3]; 4498[label="gcd1 False (Neg Zero) (Neg (Succ vuz680))",fontsize=16,color="black",shape="box"];4498 -> 4521[label="",style="solid", color="black", weight=3]; 4499[label="gcd1 True (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];4499 -> 4522[label="",style="solid", color="black", weight=3]; 4600[label="gcd1 False (Pos vuz308) (Neg (Succ vuz710))",fontsize=16,color="black",shape="box"];4600 -> 4623[label="",style="solid", color="black", weight=3]; 4601[label="gcd1 True (Pos vuz308) (Neg Zero)",fontsize=16,color="black",shape="box"];4601 -> 4624[label="",style="solid", color="black", weight=3]; 6064[label="gcd1 False (Pos Zero) (Pos (Succ vuz740))",fontsize=16,color="black",shape="box"];6064 -> 6070[label="",style="solid", color="black", weight=3]; 6065[label="gcd1 True (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];6065 -> 6071[label="",style="solid", color="black", weight=3]; 6066[label="absReal1 (Neg (Succ vuz2820)) (Neg (Succ vuz2820) >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6066 -> 6072[label="",style="solid", color="black", weight=3]; 6067[label="absReal1 (Pos vuz144) (Pos vuz144 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6067 -> 6073[label="",style="solid", color="black", weight=3]; 6068[label="gcd0Gcd'1 (primEqInt vuz373 (fromInt (Pos Zero))) vuz374 vuz373",fontsize=16,color="burlywood",shape="box"];6576[label="vuz373/Pos vuz3730",fontsize=10,color="white",style="solid",shape="box"];6068 -> 6576[label="",style="solid", color="burlywood", weight=9]; 6576 -> 6074[label="",style="solid", color="burlywood", weight=3]; 6577[label="vuz373/Neg vuz3730",fontsize=10,color="white",style="solid",shape="box"];6068 -> 6577[label="",style="solid", color="burlywood", weight=9]; 6577 -> 6075[label="",style="solid", color="burlywood", weight=3]; 4518[label="gcd0 (Neg Zero) (Pos (Succ vuz1440))",fontsize=16,color="black",shape="box"];4518 -> 4540[label="",style="solid", color="black", weight=3]; 4519 -> 4106[label="",style="dashed", color="red", weight=0]; 4519[label="error []",fontsize=16,color="magenta"];6069[label="absReal1 (Neg vuz68) (Neg vuz68 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6069 -> 6076[label="",style="solid", color="black", weight=3]; 4521[label="gcd0 (Neg Zero) (Neg (Succ vuz680))",fontsize=16,color="black",shape="box"];4521 -> 4542[label="",style="solid", color="black", weight=3]; 4522 -> 4106[label="",style="dashed", color="red", weight=0]; 4522[label="error []",fontsize=16,color="magenta"];4623 -> 4515[label="",style="dashed", color="red", weight=0]; 4623[label="gcd0 (Pos vuz308) (Neg (Succ vuz710))",fontsize=16,color="magenta"];4623 -> 4646[label="",style="dashed", color="magenta", weight=3]; 4624 -> 4106[label="",style="dashed", color="red", weight=0]; 4624[label="error []",fontsize=16,color="magenta"];6070[label="gcd0 (Pos Zero) (Pos (Succ vuz740))",fontsize=16,color="black",shape="box"];6070 -> 6077[label="",style="solid", color="black", weight=3]; 6071 -> 4106[label="",style="dashed", color="red", weight=0]; 6071[label="error []",fontsize=16,color="magenta"];6072[label="absReal1 (Neg (Succ vuz2820)) (compare (Neg (Succ vuz2820)) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];6072 -> 6078[label="",style="solid", color="black", weight=3]; 6073[label="absReal1 (Pos vuz144) (compare (Pos vuz144) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];6073 -> 6079[label="",style="solid", color="black", weight=3]; 6074[label="gcd0Gcd'1 (primEqInt (Pos vuz3730) (fromInt (Pos Zero))) vuz374 (Pos vuz3730)",fontsize=16,color="burlywood",shape="box"];6578[label="vuz3730/Succ vuz37300",fontsize=10,color="white",style="solid",shape="box"];6074 -> 6578[label="",style="solid", color="burlywood", weight=9]; 6578 -> 6080[label="",style="solid", color="burlywood", weight=3]; 6579[label="vuz3730/Zero",fontsize=10,color="white",style="solid",shape="box"];6074 -> 6579[label="",style="solid", color="burlywood", weight=9]; 6579 -> 6081[label="",style="solid", color="burlywood", weight=3]; 6075[label="gcd0Gcd'1 (primEqInt (Neg vuz3730) (fromInt (Pos Zero))) vuz374 (Neg vuz3730)",fontsize=16,color="burlywood",shape="box"];6580[label="vuz3730/Succ vuz37300",fontsize=10,color="white",style="solid",shape="box"];6075 -> 6580[label="",style="solid", color="burlywood", weight=9]; 6580 -> 6082[label="",style="solid", color="burlywood", weight=3]; 6581[label="vuz3730/Zero",fontsize=10,color="white",style="solid",shape="box"];6075 -> 6581[label="",style="solid", color="burlywood", weight=9]; 6581 -> 6083[label="",style="solid", color="burlywood", weight=3]; 4540 -> 6009[label="",style="dashed", color="red", weight=0]; 4540[label="gcd0Gcd' (abs (Neg Zero)) (abs (Pos (Succ vuz1440)))",fontsize=16,color="magenta"];4540 -> 6018[label="",style="dashed", color="magenta", weight=3]; 4540 -> 6019[label="",style="dashed", color="magenta", weight=3]; 6076[label="absReal1 (Neg vuz68) (compare (Neg vuz68) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];6076 -> 6084[label="",style="solid", color="black", weight=3]; 4542 -> 6009[label="",style="dashed", color="red", weight=0]; 4542[label="gcd0Gcd' (abs (Neg Zero)) (abs (Neg (Succ vuz680)))",fontsize=16,color="magenta"];4542 -> 6020[label="",style="dashed", color="magenta", weight=3]; 4542 -> 6021[label="",style="dashed", color="magenta", weight=3]; 4646[label="Succ vuz710",fontsize=16,color="green",shape="box"];6077 -> 6009[label="",style="dashed", color="red", weight=0]; 6077[label="gcd0Gcd' (abs (Pos Zero)) (abs (Pos (Succ vuz740)))",fontsize=16,color="magenta"];6077 -> 6085[label="",style="dashed", color="magenta", weight=3]; 6077 -> 6086[label="",style="dashed", color="magenta", weight=3]; 6078[label="absReal1 (Neg (Succ vuz2820)) (not (compare (Neg (Succ vuz2820)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6078 -> 6087[label="",style="solid", color="black", weight=3]; 6079[label="absReal1 (Pos vuz144) (not (compare (Pos vuz144) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6079 -> 6088[label="",style="solid", color="black", weight=3]; 6080[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz37300)) (fromInt (Pos Zero))) vuz374 (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6080 -> 6089[label="",style="solid", color="black", weight=3]; 6081[label="gcd0Gcd'1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz374 (Pos Zero)",fontsize=16,color="black",shape="box"];6081 -> 6090[label="",style="solid", color="black", weight=3]; 6082[label="gcd0Gcd'1 (primEqInt (Neg (Succ vuz37300)) (fromInt (Pos Zero))) vuz374 (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6082 -> 6091[label="",style="solid", color="black", weight=3]; 6083[label="gcd0Gcd'1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) vuz374 (Neg Zero)",fontsize=16,color="black",shape="box"];6083 -> 6092[label="",style="solid", color="black", weight=3]; 6018 -> 6013[label="",style="dashed", color="red", weight=0]; 6018[label="abs (Neg Zero)",fontsize=16,color="magenta"];6018 -> 6043[label="",style="dashed", color="magenta", weight=3]; 6019 -> 6011[label="",style="dashed", color="red", weight=0]; 6019[label="abs (Pos (Succ vuz1440))",fontsize=16,color="magenta"];6019 -> 6044[label="",style="dashed", color="magenta", weight=3]; 6084[label="absReal1 (Neg vuz68) (not (compare (Neg vuz68) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6084 -> 6093[label="",style="solid", color="black", weight=3]; 6020 -> 6013[label="",style="dashed", color="red", weight=0]; 6020[label="abs (Neg Zero)",fontsize=16,color="magenta"];6020 -> 6045[label="",style="dashed", color="magenta", weight=3]; 6021 -> 6013[label="",style="dashed", color="red", weight=0]; 6021[label="abs (Neg (Succ vuz680))",fontsize=16,color="magenta"];6021 -> 6046[label="",style="dashed", color="magenta", weight=3]; 6085 -> 6011[label="",style="dashed", color="red", weight=0]; 6085[label="abs (Pos Zero)",fontsize=16,color="magenta"];6085 -> 6094[label="",style="dashed", color="magenta", weight=3]; 6086 -> 6011[label="",style="dashed", color="red", weight=0]; 6086[label="abs (Pos (Succ vuz740))",fontsize=16,color="magenta"];6086 -> 6095[label="",style="dashed", color="magenta", weight=3]; 6087[label="absReal1 (Neg (Succ vuz2820)) (not (primCmpInt (Neg (Succ vuz2820)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6087 -> 6096[label="",style="solid", color="black", weight=3]; 6088[label="absReal1 (Pos vuz144) (not (primCmpInt (Pos vuz144) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];6582[label="vuz144/Succ vuz1440",fontsize=10,color="white",style="solid",shape="box"];6088 -> 6582[label="",style="solid", color="burlywood", weight=9]; 6582 -> 6097[label="",style="solid", color="burlywood", weight=3]; 6583[label="vuz144/Zero",fontsize=10,color="white",style="solid",shape="box"];6088 -> 6583[label="",style="solid", color="burlywood", weight=9]; 6583 -> 6098[label="",style="solid", color="burlywood", weight=3]; 6089[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz37300)) (Pos Zero)) vuz374 (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6089 -> 6099[label="",style="solid", color="black", weight=3]; 6090[label="gcd0Gcd'1 (primEqInt (Pos Zero) (Pos Zero)) vuz374 (Pos Zero)",fontsize=16,color="black",shape="box"];6090 -> 6100[label="",style="solid", color="black", weight=3]; 6091[label="gcd0Gcd'1 (primEqInt (Neg (Succ vuz37300)) (Pos Zero)) vuz374 (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6091 -> 6101[label="",style="solid", color="black", weight=3]; 6092[label="gcd0Gcd'1 (primEqInt (Neg Zero) (Pos Zero)) vuz374 (Neg Zero)",fontsize=16,color="black",shape="box"];6092 -> 6102[label="",style="solid", color="black", weight=3]; 6043[label="Zero",fontsize=16,color="green",shape="box"];6044[label="Succ vuz1440",fontsize=16,color="green",shape="box"];6093[label="absReal1 (Neg vuz68) (not (primCmpInt (Neg vuz68) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];6584[label="vuz68/Succ vuz680",fontsize=10,color="white",style="solid",shape="box"];6093 -> 6584[label="",style="solid", color="burlywood", weight=9]; 6584 -> 6103[label="",style="solid", color="burlywood", weight=3]; 6585[label="vuz68/Zero",fontsize=10,color="white",style="solid",shape="box"];6093 -> 6585[label="",style="solid", color="burlywood", weight=9]; 6585 -> 6104[label="",style="solid", color="burlywood", weight=3]; 6045[label="Zero",fontsize=16,color="green",shape="box"];6046[label="Succ vuz680",fontsize=16,color="green",shape="box"];6094[label="Zero",fontsize=16,color="green",shape="box"];6095[label="Succ vuz740",fontsize=16,color="green",shape="box"];6096[label="absReal1 (Neg (Succ vuz2820)) (not (primCmpInt (Neg (Succ vuz2820)) (Pos Zero) == LT))",fontsize=16,color="black",shape="triangle"];6096 -> 6105[label="",style="solid", color="black", weight=3]; 6097[label="absReal1 (Pos (Succ vuz1440)) (not (primCmpInt (Pos (Succ vuz1440)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6097 -> 6106[label="",style="solid", color="black", weight=3]; 6098[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6098 -> 6107[label="",style="solid", color="black", weight=3]; 6099[label="gcd0Gcd'1 False vuz374 (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6099 -> 6108[label="",style="solid", color="black", weight=3]; 6100[label="gcd0Gcd'1 True vuz374 (Pos Zero)",fontsize=16,color="black",shape="box"];6100 -> 6109[label="",style="solid", color="black", weight=3]; 6101[label="gcd0Gcd'1 False vuz374 (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6101 -> 6110[label="",style="solid", color="black", weight=3]; 6102[label="gcd0Gcd'1 True vuz374 (Neg Zero)",fontsize=16,color="black",shape="box"];6102 -> 6111[label="",style="solid", color="black", weight=3]; 6103[label="absReal1 (Neg (Succ vuz680)) (not (primCmpInt (Neg (Succ vuz680)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6103 -> 6112[label="",style="solid", color="black", weight=3]; 6104[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6104 -> 6113[label="",style="solid", color="black", weight=3]; 6105[label="absReal1 (Neg (Succ vuz2820)) (not (LT == LT))",fontsize=16,color="black",shape="box"];6105 -> 6114[label="",style="solid", color="black", weight=3]; 6106[label="absReal1 (Pos (Succ vuz1440)) (not (primCmpInt (Pos (Succ vuz1440)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];6106 -> 6115[label="",style="solid", color="black", weight=3]; 6107[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];6107 -> 6116[label="",style="solid", color="black", weight=3]; 6108[label="gcd0Gcd'0 vuz374 (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6108 -> 6117[label="",style="solid", color="black", weight=3]; 6109[label="vuz374",fontsize=16,color="green",shape="box"];6110[label="gcd0Gcd'0 vuz374 (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6110 -> 6118[label="",style="solid", color="black", weight=3]; 6111[label="vuz374",fontsize=16,color="green",shape="box"];6112 -> 6096[label="",style="dashed", color="red", weight=0]; 6112[label="absReal1 (Neg (Succ vuz680)) (not (primCmpInt (Neg (Succ vuz680)) (Pos Zero) == LT))",fontsize=16,color="magenta"];6112 -> 6119[label="",style="dashed", color="magenta", weight=3]; 6113[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];6113 -> 6120[label="",style="solid", color="black", weight=3]; 6114[label="absReal1 (Neg (Succ vuz2820)) (not True)",fontsize=16,color="black",shape="box"];6114 -> 6121[label="",style="solid", color="black", weight=3]; 6115[label="absReal1 (Pos (Succ vuz1440)) (not (primCmpNat (Succ vuz1440) Zero == LT))",fontsize=16,color="black",shape="box"];6115 -> 6122[label="",style="solid", color="black", weight=3]; 6116[label="absReal1 (Pos Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];6116 -> 6123[label="",style="solid", color="black", weight=3]; 6117 -> 6009[label="",style="dashed", color="red", weight=0]; 6117[label="gcd0Gcd' (Pos (Succ vuz37300)) (vuz374 `rem` Pos (Succ vuz37300))",fontsize=16,color="magenta"];6117 -> 6124[label="",style="dashed", color="magenta", weight=3]; 6117 -> 6125[label="",style="dashed", color="magenta", weight=3]; 6118 -> 6009[label="",style="dashed", color="red", weight=0]; 6118[label="gcd0Gcd' (Neg (Succ vuz37300)) (vuz374 `rem` Neg (Succ vuz37300))",fontsize=16,color="magenta"];6118 -> 6126[label="",style="dashed", color="magenta", weight=3]; 6118 -> 6127[label="",style="dashed", color="magenta", weight=3]; 6119[label="vuz680",fontsize=16,color="green",shape="box"];6120[label="absReal1 (Neg Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];6120 -> 6128[label="",style="solid", color="black", weight=3]; 6121[label="absReal1 (Neg (Succ vuz2820)) False",fontsize=16,color="black",shape="box"];6121 -> 6129[label="",style="solid", color="black", weight=3]; 6122[label="absReal1 (Pos (Succ vuz1440)) (not (GT == LT))",fontsize=16,color="black",shape="box"];6122 -> 6130[label="",style="solid", color="black", weight=3]; 6123[label="absReal1 (Pos Zero) (not False)",fontsize=16,color="black",shape="box"];6123 -> 6131[label="",style="solid", color="black", weight=3]; 6124[label="Pos (Succ vuz37300)",fontsize=16,color="green",shape="box"];6125[label="vuz374 `rem` Pos (Succ vuz37300)",fontsize=16,color="black",shape="box"];6125 -> 6132[label="",style="solid", color="black", weight=3]; 6126[label="Neg (Succ vuz37300)",fontsize=16,color="green",shape="box"];6127[label="vuz374 `rem` Neg (Succ vuz37300)",fontsize=16,color="black",shape="box"];6127 -> 6133[label="",style="solid", color="black", weight=3]; 6128[label="absReal1 (Neg Zero) (not False)",fontsize=16,color="black",shape="box"];6128 -> 6134[label="",style="solid", color="black", weight=3]; 6129[label="absReal0 (Neg (Succ vuz2820)) otherwise",fontsize=16,color="black",shape="box"];6129 -> 6135[label="",style="solid", color="black", weight=3]; 6130[label="absReal1 (Pos (Succ vuz1440)) (not False)",fontsize=16,color="black",shape="box"];6130 -> 6136[label="",style="solid", color="black", weight=3]; 6131[label="absReal1 (Pos Zero) True",fontsize=16,color="black",shape="box"];6131 -> 6137[label="",style="solid", color="black", weight=3]; 6132[label="primRemInt vuz374 (Pos (Succ vuz37300))",fontsize=16,color="burlywood",shape="box"];6586[label="vuz374/Pos vuz3740",fontsize=10,color="white",style="solid",shape="box"];6132 -> 6586[label="",style="solid", color="burlywood", weight=9]; 6586 -> 6138[label="",style="solid", color="burlywood", weight=3]; 6587[label="vuz374/Neg vuz3740",fontsize=10,color="white",style="solid",shape="box"];6132 -> 6587[label="",style="solid", color="burlywood", weight=9]; 6587 -> 6139[label="",style="solid", color="burlywood", weight=3]; 6133[label="primRemInt vuz374 (Neg (Succ vuz37300))",fontsize=16,color="burlywood",shape="box"];6588[label="vuz374/Pos vuz3740",fontsize=10,color="white",style="solid",shape="box"];6133 -> 6588[label="",style="solid", color="burlywood", weight=9]; 6588 -> 6140[label="",style="solid", color="burlywood", weight=3]; 6589[label="vuz374/Neg vuz3740",fontsize=10,color="white",style="solid",shape="box"];6133 -> 6589[label="",style="solid", color="burlywood", weight=9]; 6589 -> 6141[label="",style="solid", color="burlywood", weight=3]; 6134[label="absReal1 (Neg Zero) True",fontsize=16,color="black",shape="box"];6134 -> 6142[label="",style="solid", color="black", weight=3]; 6135[label="absReal0 (Neg (Succ vuz2820)) True",fontsize=16,color="black",shape="box"];6135 -> 6143[label="",style="solid", color="black", weight=3]; 6136[label="absReal1 (Pos (Succ vuz1440)) True",fontsize=16,color="black",shape="box"];6136 -> 6144[label="",style="solid", color="black", weight=3]; 6137[label="Pos Zero",fontsize=16,color="green",shape="box"];6138[label="primRemInt (Pos vuz3740) (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6138 -> 6145[label="",style="solid", color="black", weight=3]; 6139[label="primRemInt (Neg vuz3740) (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6139 -> 6146[label="",style="solid", color="black", weight=3]; 6140[label="primRemInt (Pos vuz3740) (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6140 -> 6147[label="",style="solid", color="black", weight=3]; 6141[label="primRemInt (Neg vuz3740) (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6141 -> 6148[label="",style="solid", color="black", weight=3]; 6142[label="Neg Zero",fontsize=16,color="green",shape="box"];6143[label="`negate` Neg (Succ vuz2820)",fontsize=16,color="black",shape="box"];6143 -> 6149[label="",style="solid", color="black", weight=3]; 6144[label="Pos (Succ vuz1440)",fontsize=16,color="green",shape="box"];6145[label="Pos (primModNatS vuz3740 (Succ vuz37300))",fontsize=16,color="green",shape="box"];6145 -> 6150[label="",style="dashed", color="green", weight=3]; 6146[label="Neg (primModNatS vuz3740 (Succ vuz37300))",fontsize=16,color="green",shape="box"];6146 -> 6151[label="",style="dashed", color="green", weight=3]; 6147[label="Pos (primModNatS vuz3740 (Succ vuz37300))",fontsize=16,color="green",shape="box"];6147 -> 6152[label="",style="dashed", color="green", weight=3]; 6148[label="Neg (primModNatS vuz3740 (Succ vuz37300))",fontsize=16,color="green",shape="box"];6148 -> 6153[label="",style="dashed", color="green", weight=3]; 6149[label="primNegInt (Neg (Succ vuz2820))",fontsize=16,color="black",shape="box"];6149 -> 6154[label="",style="solid", color="black", weight=3]; 6150[label="primModNatS vuz3740 (Succ vuz37300)",fontsize=16,color="burlywood",shape="triangle"];6590[label="vuz3740/Succ vuz37400",fontsize=10,color="white",style="solid",shape="box"];6150 -> 6590[label="",style="solid", color="burlywood", weight=9]; 6590 -> 6155[label="",style="solid", color="burlywood", weight=3]; 6591[label="vuz3740/Zero",fontsize=10,color="white",style="solid",shape="box"];6150 -> 6591[label="",style="solid", color="burlywood", weight=9]; 6591 -> 6156[label="",style="solid", color="burlywood", weight=3]; 6151 -> 6150[label="",style="dashed", color="red", weight=0]; 6151[label="primModNatS vuz3740 (Succ vuz37300)",fontsize=16,color="magenta"];6151 -> 6157[label="",style="dashed", color="magenta", weight=3]; 6152 -> 6150[label="",style="dashed", color="red", weight=0]; 6152[label="primModNatS vuz3740 (Succ vuz37300)",fontsize=16,color="magenta"];6152 -> 6158[label="",style="dashed", color="magenta", weight=3]; 6153 -> 6150[label="",style="dashed", color="red", weight=0]; 6153[label="primModNatS vuz3740 (Succ vuz37300)",fontsize=16,color="magenta"];6153 -> 6159[label="",style="dashed", color="magenta", weight=3]; 6153 -> 6160[label="",style="dashed", color="magenta", weight=3]; 6154[label="Pos (Succ vuz2820)",fontsize=16,color="green",shape="box"];6155[label="primModNatS (Succ vuz37400) (Succ vuz37300)",fontsize=16,color="black",shape="box"];6155 -> 6161[label="",style="solid", color="black", weight=3]; 6156[label="primModNatS Zero (Succ vuz37300)",fontsize=16,color="black",shape="box"];6156 -> 6162[label="",style="solid", color="black", weight=3]; 6157[label="vuz3740",fontsize=16,color="green",shape="box"];6158[label="vuz37300",fontsize=16,color="green",shape="box"];6159[label="vuz3740",fontsize=16,color="green",shape="box"];6160[label="vuz37300",fontsize=16,color="green",shape="box"];6161[label="primModNatS0 vuz37400 vuz37300 (primGEqNatS vuz37400 vuz37300)",fontsize=16,color="burlywood",shape="box"];6592[label="vuz37400/Succ vuz374000",fontsize=10,color="white",style="solid",shape="box"];6161 -> 6592[label="",style="solid", color="burlywood", weight=9]; 6592 -> 6163[label="",style="solid", color="burlywood", weight=3]; 6593[label="vuz37400/Zero",fontsize=10,color="white",style="solid",shape="box"];6161 -> 6593[label="",style="solid", color="burlywood", weight=9]; 6593 -> 6164[label="",style="solid", color="burlywood", weight=3]; 6162[label="Zero",fontsize=16,color="green",shape="box"];6163[label="primModNatS0 (Succ vuz374000) vuz37300 (primGEqNatS (Succ vuz374000) vuz37300)",fontsize=16,color="burlywood",shape="box"];6594[label="vuz37300/Succ vuz373000",fontsize=10,color="white",style="solid",shape="box"];6163 -> 6594[label="",style="solid", color="burlywood", weight=9]; 6594 -> 6165[label="",style="solid", color="burlywood", weight=3]; 6595[label="vuz37300/Zero",fontsize=10,color="white",style="solid",shape="box"];6163 -> 6595[label="",style="solid", color="burlywood", weight=9]; 6595 -> 6166[label="",style="solid", color="burlywood", weight=3]; 6164[label="primModNatS0 Zero vuz37300 (primGEqNatS Zero vuz37300)",fontsize=16,color="burlywood",shape="box"];6596[label="vuz37300/Succ vuz373000",fontsize=10,color="white",style="solid",shape="box"];6164 -> 6596[label="",style="solid", color="burlywood", weight=9]; 6596 -> 6167[label="",style="solid", color="burlywood", weight=3]; 6597[label="vuz37300/Zero",fontsize=10,color="white",style="solid",shape="box"];6164 -> 6597[label="",style="solid", color="burlywood", weight=9]; 6597 -> 6168[label="",style="solid", color="burlywood", weight=3]; 6165[label="primModNatS0 (Succ vuz374000) (Succ vuz373000) (primGEqNatS (Succ vuz374000) (Succ vuz373000))",fontsize=16,color="black",shape="box"];6165 -> 6169[label="",style="solid", color="black", weight=3]; 6166[label="primModNatS0 (Succ vuz374000) Zero (primGEqNatS (Succ vuz374000) Zero)",fontsize=16,color="black",shape="box"];6166 -> 6170[label="",style="solid", color="black", weight=3]; 6167[label="primModNatS0 Zero (Succ vuz373000) (primGEqNatS Zero (Succ vuz373000))",fontsize=16,color="black",shape="box"];6167 -> 6171[label="",style="solid", color="black", weight=3]; 6168[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];6168 -> 6172[label="",style="solid", color="black", weight=3]; 6169 -> 6331[label="",style="dashed", color="red", weight=0]; 6169[label="primModNatS0 (Succ vuz374000) (Succ vuz373000) (primGEqNatS vuz374000 vuz373000)",fontsize=16,color="magenta"];6169 -> 6332[label="",style="dashed", color="magenta", weight=3]; 6169 -> 6333[label="",style="dashed", color="magenta", weight=3]; 6169 -> 6334[label="",style="dashed", color="magenta", weight=3]; 6169 -> 6335[label="",style="dashed", color="magenta", weight=3]; 6170[label="primModNatS0 (Succ vuz374000) Zero True",fontsize=16,color="black",shape="box"];6170 -> 6175[label="",style="solid", color="black", weight=3]; 6171[label="primModNatS0 Zero (Succ vuz373000) False",fontsize=16,color="black",shape="box"];6171 -> 6176[label="",style="solid", color="black", weight=3]; 6172[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];6172 -> 6177[label="",style="solid", color="black", weight=3]; 6332[label="vuz373000",fontsize=16,color="green",shape="box"];6333[label="vuz373000",fontsize=16,color="green",shape="box"];6334[label="vuz374000",fontsize=16,color="green",shape="box"];6335[label="vuz374000",fontsize=16,color="green",shape="box"];6331[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS vuz393 vuz394)",fontsize=16,color="burlywood",shape="triangle"];6598[label="vuz393/Succ vuz3930",fontsize=10,color="white",style="solid",shape="box"];6331 -> 6598[label="",style="solid", color="burlywood", weight=9]; 6598 -> 6364[label="",style="solid", color="burlywood", weight=3]; 6599[label="vuz393/Zero",fontsize=10,color="white",style="solid",shape="box"];6331 -> 6599[label="",style="solid", color="burlywood", weight=9]; 6599 -> 6365[label="",style="solid", color="burlywood", weight=3]; 6175 -> 6150[label="",style="dashed", color="red", weight=0]; 6175[label="primModNatS (primMinusNatS (Succ vuz374000) Zero) (Succ Zero)",fontsize=16,color="magenta"];6175 -> 6182[label="",style="dashed", color="magenta", weight=3]; 6175 -> 6183[label="",style="dashed", color="magenta", weight=3]; 6176[label="Succ Zero",fontsize=16,color="green",shape="box"];6177 -> 6150[label="",style="dashed", color="red", weight=0]; 6177[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];6177 -> 6184[label="",style="dashed", color="magenta", weight=3]; 6177 -> 6185[label="",style="dashed", color="magenta", weight=3]; 6364[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS (Succ vuz3930) vuz394)",fontsize=16,color="burlywood",shape="box"];6600[label="vuz394/Succ vuz3940",fontsize=10,color="white",style="solid",shape="box"];6364 -> 6600[label="",style="solid", color="burlywood", weight=9]; 6600 -> 6366[label="",style="solid", color="burlywood", weight=3]; 6601[label="vuz394/Zero",fontsize=10,color="white",style="solid",shape="box"];6364 -> 6601[label="",style="solid", color="burlywood", weight=9]; 6601 -> 6367[label="",style="solid", color="burlywood", weight=3]; 6365[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS Zero vuz394)",fontsize=16,color="burlywood",shape="box"];6602[label="vuz394/Succ vuz3940",fontsize=10,color="white",style="solid",shape="box"];6365 -> 6602[label="",style="solid", color="burlywood", weight=9]; 6602 -> 6368[label="",style="solid", color="burlywood", weight=3]; 6603[label="vuz394/Zero",fontsize=10,color="white",style="solid",shape="box"];6365 -> 6603[label="",style="solid", color="burlywood", weight=9]; 6603 -> 6369[label="",style="solid", color="burlywood", weight=3]; 6182 -> 5741[label="",style="dashed", color="red", weight=0]; 6182[label="primMinusNatS (Succ vuz374000) Zero",fontsize=16,color="magenta"];6182 -> 6190[label="",style="dashed", color="magenta", weight=3]; 6182 -> 6191[label="",style="dashed", color="magenta", weight=3]; 6183[label="Zero",fontsize=16,color="green",shape="box"];6184 -> 5741[label="",style="dashed", color="red", weight=0]; 6184[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];6184 -> 6192[label="",style="dashed", color="magenta", weight=3]; 6184 -> 6193[label="",style="dashed", color="magenta", weight=3]; 6185[label="Zero",fontsize=16,color="green",shape="box"];6366[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS (Succ vuz3930) (Succ vuz3940))",fontsize=16,color="black",shape="box"];6366 -> 6370[label="",style="solid", color="black", weight=3]; 6367[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS (Succ vuz3930) Zero)",fontsize=16,color="black",shape="box"];6367 -> 6371[label="",style="solid", color="black", weight=3]; 6368[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS Zero (Succ vuz3940))",fontsize=16,color="black",shape="box"];6368 -> 6372[label="",style="solid", color="black", weight=3]; 6369[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];6369 -> 6373[label="",style="solid", color="black", weight=3]; 6190[label="Succ vuz374000",fontsize=16,color="green",shape="box"];6191[label="Zero",fontsize=16,color="green",shape="box"];6192[label="Zero",fontsize=16,color="green",shape="box"];6193[label="Zero",fontsize=16,color="green",shape="box"];6370 -> 6331[label="",style="dashed", color="red", weight=0]; 6370[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS vuz3930 vuz3940)",fontsize=16,color="magenta"];6370 -> 6374[label="",style="dashed", color="magenta", weight=3]; 6370 -> 6375[label="",style="dashed", color="magenta", weight=3]; 6371[label="primModNatS0 (Succ vuz391) (Succ vuz392) True",fontsize=16,color="black",shape="triangle"];6371 -> 6376[label="",style="solid", color="black", weight=3]; 6372[label="primModNatS0 (Succ vuz391) (Succ vuz392) False",fontsize=16,color="black",shape="box"];6372 -> 6377[label="",style="solid", color="black", weight=3]; 6373 -> 6371[label="",style="dashed", color="red", weight=0]; 6373[label="primModNatS0 (Succ vuz391) (Succ vuz392) True",fontsize=16,color="magenta"];6374[label="vuz3940",fontsize=16,color="green",shape="box"];6375[label="vuz3930",fontsize=16,color="green",shape="box"];6376 -> 6150[label="",style="dashed", color="red", weight=0]; 6376[label="primModNatS (primMinusNatS (Succ vuz391) (Succ vuz392)) (Succ (Succ vuz392))",fontsize=16,color="magenta"];6376 -> 6378[label="",style="dashed", color="magenta", weight=3]; 6376 -> 6379[label="",style="dashed", color="magenta", weight=3]; 6377[label="Succ (Succ vuz391)",fontsize=16,color="green",shape="box"];6378 -> 5741[label="",style="dashed", color="red", weight=0]; 6378[label="primMinusNatS (Succ vuz391) (Succ vuz392)",fontsize=16,color="magenta"];6378 -> 6380[label="",style="dashed", color="magenta", weight=3]; 6378 -> 6381[label="",style="dashed", color="magenta", weight=3]; 6379[label="Succ vuz392",fontsize=16,color="green",shape="box"];6380[label="Succ vuz391",fontsize=16,color="green",shape="box"];6381[label="Succ vuz392",fontsize=16,color="green",shape="box"];} ---------------------------------------- (435) TRUE